CN113869648A - MIMO radar resource scheduling method based on PSO optimization algorithm - Google Patents

Abstract

The invention discloses a PSO optimization algorithm-based MIMO radar resource scheduling method, which comprises the following steps: constructing a resource scheduling optimization model of the MIMO radar in the MISO mode based on the radar task structure and the radar resource constraint condition; solving the optimization model by utilizing a PSO optimization algorithm based on an entropy value; and outputting an optimal scheduling sequence according to the solution of the optimal model, and arranging the execution sequence of each task on the time axis according to the obtained optimal scheduling sequence. The PSO optimization algorithm is based on the algorithm, and the global search performance of the algorithm is ensured through chaotic initialization and entropy value optimization search parameters; under the framework of intelligent search, heuristic rules are adopted for nesting, so that the waiting period and the receiving period of the task can be efficiently utilized. Finally, the advantages of the proposed algorithm compared with the existing resource scheduling algorithm are proved through a large number of simulations.

Description

MIMO radar resource scheduling method based on PSO optimization algorithm

Technical Field

The invention relates to the technical field of radar systems, in particular to a MIMO radar resource scheduling method based on a PSO optimization algorithm.

Background

The MIMO radar can simultaneously transmit a plurality of beams, and each beam independently executes respective tasks in space, thereby realizing simultaneous multiple functions in the real sense. Compared with a time division multiplexing system of the traditional phased array radar, the MIMO radar has the following obvious advantages in simultaneous multi-beam:

first, by transmitting a wide beam while performing a search task, a wider spatial range can be covered at the same time; the beam pattern is not superposed in the space, so that the low interception requirement in military operation is indirectly met;

secondly, when multiple tasks are executed, each beam can independently execute the task, so that the hardware requirement of the system is reduced, and better signal processing performance can be obtained;

thirdly, the signals in the multiple beams can be separated in time, space and polarization domains, and the method has the advantages of large processing freedom, high aperture utilization rate and the like.

After the MIMO radar system completes resource allocation, a scheduling sequence needs to be designed to arrange an execution order of a plurality of tasks on the time axis. However, due to the hardware limitations of the radar system, such as the scheduling interval, the heat dissipation performance of the transmitter, etc., if the task sequence to be executed is randomly arranged, it is difficult to take advantage of the multiple functions of the MIMO radar. Under this condition, an efficient task scheduling algorithm is required.

However, the scheduling algorithm proposed for the resource scheduling problem of radar still has the following problems:

firstly, a universal optimized task scheduling model cannot be established;

secondly, in order to simplify modeling, only the same task is considered to be executed in parallel; in practice, the MIMO radar can realize the mutual overlapping of different tasks on a time axis;

thirdly, the built loop nesting algorithm inevitably has vacant time intervals, which causes the waste of partial time resources;

fourthly, the adopted solving method belongs to a heuristic algorithm, the algorithm only seeks the optimal solution which can be found in each iteration according to heuristic rules, and a parallel search mechanism is not provided, so that the algorithm is easy to fall into local extreme points, and the global optimal solution is difficult to obtain.

Disclosure of Invention

Aiming at the existing problems, the invention provides a Particle Swarm Optimization (PSO) based on an entropy value, and the PSO based on the improved PSO realizes MIMO radar resource scheduling, and in order to realize the purpose, the technical scheme adopted by the invention is as follows:

the MIMO radar resource scheduling method based on the PSO optimization algorithm is characterized by comprising the following steps:

step 1: constructing an optimized model of resource scheduling in an MISO mode of the MIMO radar based on a radar task structure and a radar resource constraint condition;

step 2: solving the optimization model by utilizing a PSO optimization algorithm based on an entropy value;

and step 3: and outputting an optimal scheduling sequence according to the solution of the optimal model, and arranging the execution sequence of each task on the time axis according to the obtained optimal scheduling sequence.

Further, the radar task structure described in step 1 includes three subtasks: a transmission period, a waiting period, and a reception period, the kth radar task is represented as:

T_k＝{P_k,t_ak/t_ek,t_xk,t_wk,t_rk,P_tk,t_dwk,w_k,t_dk,Δt_k} (1)，

wherein, P_kIs priority, t_akIs the request time, t_ekIs execution time, t_xkIs the emission period, t_wkIs a waiting period, t_rkIs a reception period, t_dwkIs the dwell time, w_kIs a time window, t_dkIs a cut-off period, Δ t_kThe request interval of two same adjacent tasks;

and a dwell time t_dwkSatisfies the following conditions:

t_dwk＝t_xk+t_wk+t_rk (2)，

end period t_dkSatisfies the following conditions:

t_dk＝t_ak+w_k (3)，

request interval Δ t_kSatisfies the following conditions:

t_ak＝t_e(k-1)+Δt_k (4)。

further, the resource scheduling optimization model in step 1 includes an objective function and a resource constraint condition, where the objective function of resource scheduling in the MISO mode of the MIMO radar is:

the resource constraint conditions are as follows:

s.t.

t_dwk＝t_xk+t_wk+t_rk (19)，

t_dk＝t_ak+w_k (20)，

t_end＝t_start+t_SI (21)，

max(t_ak-w_k,t_start)≤λ_kt_ek≤min(t_dk,t_end-t_dwk) (22)，

ξ_iλ_it_ei≥ξ_kλ_k(t_ek+t_xk+t_wk+t_rk) (23)，

i,k＝1,2,...N,i≠k (30)，

t_ai+w_i≥t_end (35)，

t_ai+w_i＜t_end (36)，

wherein, t_startAnd t_endRespectively the start and end times, t, of the SI_SIIs the SI time length, the SI is the minimum time unit of radar task scheduling,

is a power threshold, P_τ(t) is the power consumption value of the radar at the time t, and p (x) is the instantaneous power consumption of the radar; τ is a backoff parameter.

Further, the entropy-based PSO optimization algorithm of step 2 includes:

step 21: initializing parameters, generating a chaotic sequence by adopting a Logistic equation based on the initialized parameters, optimizing an initialized population, and generating the chaotic sequence according to the formula:

η(q+1)＝μη(q)[1-η(q)] (46)，

wherein eta (q) is a result of iteration of a chaos variable eta for q times, and eta belongs to [0,1 ]; mu is a control parameter of the chaotic state, and mu belongs to [0,4 ];

and μ ═ 4, and,

step 22: adopting a heuristic interleaving algorithm to interleave and schedule tasks of different types;

step 23: expressing the diversity of the population genes by using an entropy value, and performing iterative optimization by using a PSO algorithm;

step 24: in the iterative optimization process, the cross probability P in the GA algorithm is measured by using the entropy value_cAnd the mutation probability P_mOptimizing and selecting the ones with poorer adaptive values when performing the crossover operation

The particles are used as parents and randomly selected in mutation operation

Individual granuleThe child is used as a parent, and the population diversity is improved through the crossing and mutation operations;

step 25: judging t is more than or equal to t_maxAnd if so, directly outputting the optimal scheduling sequence, and if not, turning to the step 22 to continue iteration.

Further, the heuristic interleaving algorithm described in step 22 includes the following steps:

step 221: setting N genes of the population to be arranged in ascending order, wherein the number of the arranged request tasks is N, and the time axis of the SI is [ t ]_start,t_end]The ith time slice occupied by the receive period of the scheduled task is [ t ]_rsi,t_rei]And i is equal to 1,2, …, m, m is less than or equal to n, and the time pointer of the end time of the nth task transmitting period which indicates the latest successful scheduling is t_xenThe power pointer indicating the power consumption after the end of the most recently successfully scheduled task is P_t0The rest N-N request tasks are respectively coded into tasks 0,1,2, … and N-N-1;

step 222: at t_e0When the task 0 is scheduled at any moment, time feasibility detection is respectively carried out on the transmitting period and the receiving period of the task 0, if the transmitting period and the receiving period both meet corresponding time constraints, energy feasibility detection is carried out on the task 0, and if the time feasibility detection and the energy feasibility detection both meet the requirements, the task 0 is carried out at t_e0The time can be successfully scheduled;

in particular, the amount of the solvent to be used,

the time feasibility test for the emission period is as follows:

when the transmission of task 0 expires equation (37), (38), or (39), then the time constraint is satisfied;

the time feasibility detection in the receiving period is as follows:

t_e0+t_x0+t_w0+t_r0≤t_end (40)，

when the receipt of task 0 expires, equation (40), then the time constraint is satisfied;

the energy feasibility test is as follows:

when task 0 satisfies equation (41), then the energy constraint is satisfied;

and when

When, task 0 is at t_e0The time can be successfully scheduled;

step 223: updating the time index to t_e0+t_x0Updating the power pointer P_t0Is P_testAnd updating the time slice occupied by the receiving period of the scheduled task to be t_rs0,t_re0]∪[t_rsi,t_rei](i ═ 1,2, …, m), thereby achieving interleaving of scheduled tasks.

Further, the specific operation steps of step 23 include:

step 231: the population diversity is represented by entropy values: setting the population base number to N_popEach particle individually comprises N genes, N_popThe set of jth gene in the individual is j, and the number of jth gene in j of ith particle is b_ijThen the probability of the gene in the population is:

P_ij＝b_ij/N_pop (48)，

the entropy of the gene is:

the diversity of the population can be represented by the mean entropy:

step 232: setting the inertia weight w in the PSO algorithm by the mean entropy of the genes:

in the formula, w_min、w_maxUpper and lower bounds of the inertial weight, respectively;

step 233: optimizing in a discrete domain by using a PSO algorithm: setting the minimum discrete time unit to Δ t_pThe velocity and position of each individual is updated using equations (43) and (45):

in the formula,

and

respectively the position and velocity vector, p, of the particle_best(t) the best solution found so far for each particle; g_best(t) is the optimal solution found so far for the population of particles; r is₁、r₂Is a random number between 0 and 1; c. C₁And c₂Is a cognitive parameter, and c₁＝c₂＝2，round (.) is the rounding operation.

Further, the optimizing the crossover and mutation probabilities by using entropy values in step 24 includes:

optimizing the cross probability:

wherein, P_cmaxAnd P_cminThe upper and lower bounds of the cross probability are respectively;

and (3) mutation probability optimization:

wherein, P_mmaxAnd P_mminThe upper and lower bounds of the variation probability are respectively.

The invention has the beneficial effects that:

the invention provides a PSO optimization algorithm-based MIMO radar resource scheduling method, and a 0-1 integer programming model is established for the MIMO radar resource scheduling problem in an MISO mode. And the multi-dimensional NP problem is efficiently solved by utilizing a PSO optimization algorithm based on an entropy value. The global search performance of the algorithm is ensured by chaotic initialization and entropy value optimization search parameters; under the framework of intelligent search, heuristic rules are adopted for nesting, so that the waiting period and the receiving period of the task can be efficiently utilized. Simulation results show that compared with the existing three scheduling algorithms (online interleaving algorithm, hybrid genetic-particle swarm algorithm and high priority algorithm), the algorithm provided by the invention achieves better scheduling results and more stable scheduling performance.

Drawings

FIG. 1 is a flow chart of an entropy-based PSO optimization algorithm proposed by the present invention;

FIGS. 2(a) - (c) are a sequence of requested tasks, a sequence of scheduling of requested tasks using the method of the present invention, and a sequence of scheduling of tasks using an optimization model, respectively;

FIG. 3 is an entropy-based PSO optimization algorithm convergence diagram proposed by the present invention;

FIG. 4 is a graph comparing the scheduling success rates of the algorithms in the embodiment;

FIG. 5 is a comparison graph of the realized value rates of the algorithms in the example;

FIG. 6 is a graph comparing the time utilization of the algorithms in the examples;

FIG. 7 is a graph comparing time shift rates of the algorithms in the examples;

FIG. 8 is a schematic diagram of an exemplary radar mission configuration;

FIGS. 9(a) - (g) illustrate the task scheduling in MISO and SISO modes.

Detailed Description

In order to make those skilled in the art better understand the technical solution of the present invention, the following further describes the technical solution of the present invention with reference to the drawings and the embodiments.

Entropy is a powerful tool to measure system uncertainty. When the uncertainty of the system is strong, the information entropy is large; otherwise, the information entropy is smaller. Similarly, the PSO population can also be regarded as a system, and when the population diversity is strong, the entropy value is large; when the population tends to be consistent, the entropy value is smaller. Therefore, the invention provides an entropy-based PSO optimization algorithm in combination with task scheduling characteristics in the MISO mode to improve the global optimization capability of the PSO, and the PSO optimization algorithm based on the entropy is utilized to schedule MIMO radar resources.

From the exemplary radar task structure shown in fig. 8, it can be seen that a radar task is composed of three subtasks: a transmit period, a wait period, and a receive period. The kth radar task may be represented by the following 10-element array:

T_k＝{P_k,t_ak/t_ek,t_xk,t_wk,t_rk,P_tk,t_dwk,w_k,t_dk,Δt_k} (1)，

the respective parameters in the formula (1) are explained as shown in Table 1:

TABLE 1 task parameters and explanations

Wherein the dwell time t_dwkSatisfies the following conditions:

t_dwk＝t_xk+t_wk+t_rk (2)，

end period t_dkSatisfies the following conditions:

t_dk＝t_ak+w_k (3)，

w in the formula (3)_kIs the time window for task k. All request tasks can only be valid if they are successfully scheduled within their respective time window; otherwise, it will lose meaning due to the maneuver of the target.

And Δ t_kSatisfies the following conditions:

t_ak＝t_e(k-1)+Δt_k (4)，

t in formula (4)_akThe request time of the task is also the best execution time; t is t_e(k-1)And the execution time of the last successfully scheduled task of the same type is obtained.

And the constraint model of the radar resource is as follows:

1. time constraints

And the SI is the minimum time unit of radar task scheduling. In one SI, the radar needs to process the echo signal in the last SI and call a scheduling algorithm to determine the task execution sequence in the next SI. After analysis, the scheduling algorithm divides the tasks into three subsets: executing tasks, deleting tasks and delaying tasks. Tasks in the first two subsets are executed and deleted respectively, and the delayed tasks are delayed to the subsequent SI to be used as the request tasks again. Wherein all execution tasks must satisfy the following constraints:

max(t_start,t_ak-w_k)≤t_ek≤min(t_dk,t_end-t_dwk) (5)，

t in formula (5)_startAnd t_endRespectively the start time and the end time of the SI, and satisfies t_end＝t_start+t_SI；t_SIIs the SI duration.

As can be seen from the above equation, the task to be executed needs to satisfy not only the constraint of SI but also the limitation of the time window.

2. Scheduling mode constraints

Fig. 9(c) - (f) show task scheduling diagrams in the MISO mode, in which the hatched rectangle represents task k and the blank rectangle represents task i. And it can be seen from fig. 9(c) - (f) that the transmitting or receiving subtasks of the radar can be performed alternately in the waiting period, and at the same time, a plurality of receiving periods can be overlapped with each other on the time axis. In addition, due to the diversity of the operation modes of the MIMO radar, the SISO modes represented by fig. 9(a), 9(b), and 9(g) are also applicable to the MIMO radar. Under this condition, the constraints corresponding to fig. 9(a) to (g) can be expressed as formulas (6) to (12), respectively:

ξ_it_ei≥ξ_k(t_ek+t_xk+t_wk+t_rk) (6)，

where xi, ρ, τ,

χ, ψ, ω are {0,1} parameters, and the subscripts i, ei, k thereof respectively represent the cases where the corresponding constraints are satisfied in the diagrams (a) to (g), and these parameters satisfy:

wherein i ≠ 1,2 … N, k ≠ 1,2, … N, and i ≠ k; n is the number of requesting tasks within one SI.

3. Restraint of energy dissipation

In the process of task sequential execution, each task needs to generate certain energy. Due to the limitations of the physical conditions of the transmitter, the effect of energy dissipation must be considered to ensure that the transmitter is not damaged by excessive temperatures, i.e.:

wherein,

is a power threshold; p_τAnd (t) is the power consumption value of the radar at the time t.

And P is_τ(t) can be characterized in exponential form:

where p (x) is the instantaneous power consumption of the radar; tau is a backspacing parameter and represents the heat dispersion of the radar;

to this end, equations (6) - (15) together form a mathematical model of radar resource scheduling, and each equation is a scheduling constraint.

As can be seen from the formula (14),

an upper limit is set for the continuous execution of tasks, which must be suspended to protect the transmitter when a threshold is exceeded.

In the task scheduling process, the following three principles need to be satisfied:

(1) the importance principle, namely that hardware resources need to be preferentially allocated to more important tasks;

(2) an urgency principle, that is, available resources need to be preferentially allocated to more urgent tasks;

(3) the timeliness principle, i.e. the actual execution time of a task needs to be as close as possible to its requested execution time to cope with dynamic changes in the target.

The first two principles reflect the inherent attributes of radar tasks, and the third principle reflects the relationship between the scheduling algorithm and the radar tasks. From Table 1, the priority P of the task_kAnd a deadline t_dkThe importance and urgency of the task are characterized separately. Therefore, a generic objective function for the scheduling schemes in MISO mode and SISO mode is constructed:

o(P_k,t_ak,w_k,t_start,t_ek)＝[o₁(P_k)+o₂(t_ak,w_k,t_start)]o₃(t_ek,t_ak,w_k) (17)，

lambda in the formula_kE {0,1}, which is a binary variable.

When task T_kWhen not scheduled, λ _k0; when task T_kIs successfully scheduledWhen is lambda_k＝1。

o₁(P_k) For task priority P_kAn increasing function of; o₂(t_ak,w_k,t_start) For task deadline t_dkAnd SI start time t_startA decreasing function of the relative distance between; o₃(t_ek,t_ak,w_k) Requesting a time t for a task_akAnd the actual execution time t_ekIn a time window w_kAnd the function of the internal relative distance represents the timeliness of task scheduling. The smaller the relative distance, the more timely the task is performed.

Therefore, on the basis of the above, the resource scheduling problem in the MISO mode can be expressed as:

s.t.

t_dwk＝t_xk+t_wk+t_rk (19)，

t_dk＝t_ak+w_k (20)，

t_end＝t_start+t_SI (21)，

max(t_ak-w_k,t_start)≤λ_kt_ek≤min(t_dk,t_end-t_dwk) (22)，

ξ_iλ_it_ei≥ξ_kλ_k(t_ek+t_xk+t_wk+t_rk) (23)，

i,k＝1,2,...N,i≠k (30)，

in addition, when the request task is not successfully scheduled, the request task is delayed to the subsequent SI or is directly deleted. Therefore, the following conditions should also be taken into account:

t_ai+w_i≥t_end (35)，

t_ai+w_i＜t_end (36)，

equations (35) and (36) correspond to the constraint conditions, t, for the delayed task and the deleted task, respectively_aiIs the request time of task i, w_iIs the time window for task i.

Obviously, the resource scheduling problem in the MISO mode is a typical multi-dimensional NP problem, so the invention provides a PSO optimization algorithm based on entropy to solve the optimization model.

The flow chart of the PSO optimization algorithm based on the entropy value is shown in the attached figure 1, and comprises the following steps:

step 1: initializing parameters;

step 2: the adaptive value is calculated based on a heuristic interleaving algorithm, which can not only interleave different types of tasks, but also realize the mutual overlapping of receiving periods of different types of tasks, provide a shortcut for the calculation of the individual adaptive value and reduce the calculation burden of a PSO algorithm;

and step 3: combining PSO and GA algorithm, and performing iterative optimization for searching a more optimal solution set; the combined hybrid algorithm has the advantages of fast PSO convergence and global GA optimization, so that the solving capability and efficiency of the algorithm are improved;

and 4, step 4: introducing an entropy value to indicate the diversity of the population, and adaptively adjusting search parameters to balance the local search capability and the global optimization performance of the population;

and 5: judging whether the iteration number t is more than or equal to t_maxAnd if so, directly outputting the optimal scheduling sequence, and if not, turning to the step 2 to continue iteration.

The heuristic task interleaving algorithm achieves the purpose of rapidly solving the individual adaptive value by decomposing the feasibility analysis of task scheduling into two parts, namely time feasibility detection and energy feasibility detection.

Suppose that N genes of the population (corresponding to the times to be scheduled of the N request tasks) have been arranged in ascending order and the number of successfully scheduled request tasks is N. Time axis of SI is [ t ]_start,t_end](ii) a The ith time slice occupied by the receiving period of the scheduled task is t_rsi,t_rei]And i is 1,2, …, m, m is less than or equal to n. The time pointer for indicating the end time of the nth task transmission period which is successfully scheduled recently is t_xen(ii) a The power pointer indicating the power consumption after the end of the most recently successfully scheduled task is P_t0. The remaining N-N request tasks are respectively organized as tasks 0,1,2, …, N-N-1.

When trying at t_e0When scheduling the task 0 at any moment, firstly, performing time feasibility detection on the transmission period:

when the transmission of task 0 expires equation (37), (38), or (39), then the time constraint is satisfied. Then, the reception period of task 0 is detected using equation (40):

t_e0+t_x0+t_w0+t_r0≤t_end (40)，

when the receiving period of task 0 also satisfies the time constraint, the energy feasibility detection is further performed:

when in use

When, task 0 is at t_e0The time of day may be successfully scheduled.

Thereafter, the time pointer t is updated_xenIs t_e0+t_x0Updating the power pointer P_t0Is P_testAnd updating the time slice occupied by the receiving period of the scheduled task to be t_rs0,t_re0]∪[t_rsi,t_rei](i＝1,2,…,m)。

Through the continuous updating of the time indicator, the power indicator and the time slice occupied by the successfully scheduled task receiving period, the specific mode of task staggered execution can be omitted, and therefore the feasibility analysis of task scheduling is greatly simplified.

In performing the iterative optimization, a PSO algorithm is used, and generally each individual in the PSO algorithm updates its own velocity and position using equations (43) and (44):

in the formula,

and

respectively the position and velocity vectors of the particles; p is a radical of_best(t) the best solution found so far for each particle; g_best(t) is the optimal solution found so far for the population of particles; r1 and r2 are random numbers between 0 and 1; c1 and c2 are cognitive parameters and can adjust the particle direction p_best(t) and g_best(t) maximum step size of flight, usually taken as c₁＝c₂2; w is an inertia weight, and the global optimizing and local searching capability of the algorithm is balanced.

The PSO algorithm is intended to solve the optimization problem of continuous variables, however, for radar systems, optimization in a discrete domain is required to meet the real-time requirement. Therefore, the search dimension can be reduced, and the solving efficiency is improved. If the minimum discrete time unit is set to Δ t_pThen, then

Can be calculated using the following formula:

where round (.) is the rounding operation. Due to p_best(t +1) and g_best(t +1) are all from

Then the elements in both are also Δ t_pInteger multiples of.

In order to avoid premature convergence of the PSO algorithm in the searching process, the algorithm is optimized by utilizing chaotic initialization and entropy optimization, so that the algorithm is prevented from falling into a local extreme value.

Firstly, because the chaotic system is full of instability and randomness, the chaotic system can be used for improving the global search performance of a PSO algorithm, the chaotic system utilizes initialized parameters and adopts a Logistic equation to generate a chaotic sequence:

η(q+1)＝μη(q)[1-η(q)] (46)，

in the formula, eta (q) is a result of iteration of a chaos variable eta for q times, and eta belongs to [0,1 ]; mu is a control parameter of the chaotic state, and mu belongs to [0,4 ];

when mu is 4 and

and meanwhile, the generated sequence has the complete chaotic characteristic, and the track of the chaotic variable eta is distributed in the whole solution space.

Let the upper and lower bounds of the jth gene on an individual be t_maxjAnd t_minjAnd both can be derived from equation (5), then the solution variables need to be mapped to [0,1]Interval:

t′_ej＝(t_ej-t_minj)/(t_maxj-t_minj) (47)，

in the formula, t_ejRepresents the jth gene, namely the candidate execution time of the jth task. Then, in iteration q_maxThen, t 'is added'_ejRemap back to original interval [ t ]_minj,t_maxj]. It should be noted that during the PSO algorithm search, each gene must always be within the feasible interval.

The chaotic sequence can improve the local optimal search performance of the PSO. The solving variables are mapped into the [0,1] interval through the formula (47), and each gene is guaranteed to be always located in a feasible interval in the PSO algorithm calculation process.

In order to represent the diversity of the population and realize the self-adaptive adjustment of the algorithm search parameters, the invention utilizes the entropy value to represent, when the entropy value is higher, the diversity of the population genes is stronger, and when the entropy value is lower, the genes tend to be similar.

Assuming a population base number of N_popEach particle contains N genes. N is a radical of_popThe set of jth gene in the individual is j, and the number of jth gene in j of ith particle is b_ij. Then the probability of the gene in the population is:

P_ij＝b_ij/N_pop (48)，

the entropy of the gene is:

and the diversity of the population can be represented by the mean entropy:

in the PSO algorithm, the inertial weight w balances the local search and global search capabilities of the algorithm. In the initial stage, the larger inertia weight can position the approximate range of the optimal solution faster; and in the later searching stage, the smaller inertia weight can improve the searching precision of the algorithm. Meaning g in view of larger average entropy_best(t) is farther from the optimal solution and smaller averageEntropy then means g_best(t) is closer to the optimal solution, so the inertial weight is set to:

in the formula, w_min、w_maxUpper and lower bounds of the inertial weight, respectively.

From equation (51), it can be seen that w can be adjusted according to the diversity of the population to balance the search performance of the algorithm locally and globally in real time.

When all particles reach the local extremum, the PSO algorithm stops iterating. Therefore, the invention adopts crossover and mutation operators in GA to improve the diversity of the population;

the GA algorithm simulates the evolution mechanism of the natural organisms, and the algorithm retains superior solutions and eliminates inferior solutions through continuous selection, intersection and variation operations so as to achieve the aim of global optimization. In the process of optimizing, the selected individuals are called parents, and the individuals generated through the operations of crossing and mutation are called offspring. In order to improve the adaptivity of the algorithm, the cross probability and the mutation probability are optimized by using entropy values as well:

in the formula, P_cmaxAnd P_cminThe upper and lower bounds of the cross probability are respectively; p_mmaxAnd P_mminThe upper and lower bounds of the variation probability are respectively.

Equations (52) and (53) show that when population diversity decreases, more individuals will be changed by crossover, mutation operations, thereby ensuring the global convergence performance of the algorithm.

Selecting the one with poor adaptive value during the cross operation

The particles are used as parents, and genes on the two parents are randomly and alternately exchanged in a non-repeated way. In mutation operations, random selection

Taking each particle as a parent, and performing gene updating on each individual by adopting a formula (54), namely updating the positions of the particles in the PSO algorithm:

in the formula,

is a rounding-down operation; as a Hardmard product; randn is a pseudo-random sequence that follows a standard normal distribution.

Examples

In order to further verify the effectiveness and the reasonability of the method, the performance of the algorithm is verified by using a small-scale example.

Assuming that there are 24 requesting tasks within one SI, the sequence of requesting tasks, the sequence of scheduling the requesting tasks using the proposed algorithm, and the sequence of scheduling the tasks using the optimization model are shown in fig. 2(a) - (c). Specific request task parameters and scheduling sequence parameters are shown in tables 2 and 3, respectively. Furthermore, fig. 3 gives a convergence diagram of the proposed algorithm.

In fig. 2(a) - (c), the horizontal axis represents time, the vertical axis represents task priority, and each rectangle represents a transmission period or a reception period of a task. Fig. 2(b) shows a scheduling sequence obtained by using the algorithm of the present invention, and it can be seen that the algorithm not only fully utilizes the waiting period to interleave other subtasks, but also implements mutual overlapping of different receiving periods to maximize time utilization. Moreover, the algorithm integrates task staggering and search optimization, so that all request tasks are successfully scheduled; at the same time, ATSR is better controlled at 0.0846.

FIG. 2(c) isAnd solving the task scheduling sequence obtained by the optimization model by using a branch and bound algorithm. Although its scheduling sequence is consistent with the algorithm results presented in the present invention. However, it requires a large amount of calculation (about 10) to solve the optimization model⁵s), therefore, it is difficult to be practically used.

TABLE 2 request task parameters

TABLE 3 scheduling sequence parameters

Simulation verification is performed by using a simulation framework, and the target number indicates the radar load under different conditions.

Let t_SI＝50ms，

τ＝200ms，T_total50 s. The objective function is chosen as: o₁(P_k)＝P_k，o₂(t_ak,w_k,t_start)＝exp[-2(t_ak+w_k-t_start)/t_SI]，o₃(t_ek,t_ak,w_k)＝(1-|t_ek-t_ak|/w_k). The task parameters are shown in table 4.

TABLE 5.4 task parameters

In the simulation, the following algorithms are compared: (1) an online interleaving algorithm; (2) a hybrid genetic-particle swarm algorithm; (3) high qualityPriority-first algorithm. In the proposed algorithm, set N_pop＝100，w_max＝0.9，w_min＝0.2，P_cmax＝0.6，P_cmin＝0.2，P_mmax＝0.4，P_mmin＝0.05，t_max＝200，q＝3000，Δt_p0.25 ms. In the hybrid genetic-particle swarm algorithm, N_pop＝100，w_max＝0.9，w_min＝0.2，P_c＝0.5，P_m＝0.1，t _max200. It should be noted that the high priority algorithm and the on-line interleaving algorithm only have Δ t as parameters_p. The statistical results after 100 simulation experiments are shown in fig. 4 to 7.

Fig. 4 is a graph comparing the scheduling success rates of the algorithms. As the number of targets increases, the available space on the radar timeline continues to shrink and more requested tasks are abandoned. The high priority algorithm does not take into account the interleaved execution of tasks, and the requesting tasks quickly fill the timeline, thus the largest number of requesting tasks are discarded. The hybrid genetic-particle swarm algorithm utilizes the waiting period of the task to execute the task in a staggered mode, but does not consider the characteristic that different receiving periods can be overlapped with each other in a MISO mode, so that the scheduling success rate is not high. The line interleaving algorithm only overlaps the receiving periods of the tasks with the same repetition period, so that more idle time is left on the radar time axis. The algorithm provided by the invention can realize the mutual overlapping of any kind of task receiving periods under the condition of meeting the constraint, so that the algorithm provided by the invention has better performance than an online staggered algorithm, and the scheduling success rate of the algorithm provided by the invention is highest.

Figure 5 compares the realized value rates of the four algorithms. Similar to the scheduling success rate, the high priority algorithm does not effectively utilize the waiting period of the tasks, so that a large number of tasks are abandoned, and the realization value rate is also the lowest. The hybrid genetic-particle swarm algorithm allows for the staggered execution of tasks, and therefore, the realization cost rate is slightly high. Although the online interleaving algorithm enables the receiving periods of the tasks to be overlapped on the basis of interleaving the tasks by using the waiting period, the realization cost rate is only slightly higher than that of the hybrid genetic-particle swarm algorithm. This shows that the online interleaving algorithm finds only a locally optimal solution. Compared with a hybrid genetic-particle swarm algorithm, the algorithm provided by the invention has the advantage that the realization value rate is greatly improved. The main reason is that the proposed algorithm utilizes a population search framework to ensure global optimization performance, and adopts a heuristic interleaving technique to fully utilize the waiting period and the receiving period of the task.

FIG. 6 is a comparison of time utilization. It can be seen that the divergence points of the three reference algorithms and the algorithm proposed by the present invention are consistent with those in fig. 4 and 5, and the side surface proves the correctness of the observed result. In addition, the algorithm provided by the invention still obtains the optimal scheduling performance.

Fig. 7 compares the time offset rates of the four algorithms. Compared with a hybrid genetic-particle swarm algorithm and the algorithm, the time offset rate of the high-priority algorithm and the online interleaving algorithm is higher. The reason is that the latter two algorithms adopt heuristic rules and preferentially schedule tasks meeting preset conditions. In contrast, the time offset rate of the algorithm provided by the invention is the lowest. The heuristic interleaving algorithm is used for efficiently utilizing the receiving period and the waiting period of different tasks; at the same time, the PSO optimization algorithm based on entropy provides a high quality solution set. Therefore, the requesting tasks are all scheduled in time.

Tables 5 to 8 show the comparison of standard deviations of the respective evaluation indexes. Although the parameters of interest for each index are different, some general conclusions can be drawn:

(1) the standard deviation of each algorithm gradually increases as the number of targets increases. Because the dispatching environment is more complicated due to the targets of more batches, more uncertainty is brought to the algorithm;

(2) the standard deviation of the transform-heuristic algorithms (i.e., hybrid genetic-particle swarm algorithm and the proposed algorithm) is small, while the stability of the heuristic algorithms (online interleaving algorithm and high priority algorithm) is poor. The reason is that the heuristic algorithm has no parallel search mechanism, only depends on heuristic rules to carry out optimization, and is easy to fall into local extreme points. Moreover, when facing larger-scale request tasks, the performance of the algorithm is obviously reduced. The transformation-heuristic algorithm depends on individual cooperation and iterative search, and a better result can be often found;

(3) compared with a hybrid genetic-particle swarm algorithm, the algorithm provided by the invention has more stable performance. This is because the heuristic interleaving technique in the proposed algorithm takes full advantage of the latency and the reception of the requesting task, thus obtaining greater scheduling flexibility. In addition, the algorithm provided by the invention applies various optimization techniques, such as chaotic initialization, entropy optimization and the like, so that the global optimality of the result is ensured.

Through a large number of simulation experiments, the optimal parameters of the algorithm can be determined as follows: n is a radical of_pop＝100，w_max＝0.7～0.9，w_min＝0.1～0.3，P_cmax＝0.4～0.6，P_cmin＝0.15～0.25，P_mmax＝0.2～0.4，P_mmin0.05 to 0.1. Although other parameters can provide high-quality scheduling results, sometimes the algorithm has problems of too long running time, falling into local extrema and the like, and the above parameters are more stable in comparison.

TABLE 5 Standard Difference of scheduling success (× 10)^-2)

TABLE 6 Standard deviation of achievement Rate (. times.10)^-2)

TABLE 7 Standard deviation of time utilization (× 10)^-2)

TABLE 8 standard deviation of time offset ratio (× 10)^-2)

The foregoing shows and describes the general principles, essential features, and advantages of the invention. It will be understood by those skilled in the art that the present invention is not limited to the embodiments described above, which are described in the specification and illustrated only to illustrate the principle of the present invention, but that various changes and modifications may be made therein without departing from the spirit and scope of the present invention, which fall within the scope of the invention as claimed. The scope of the invention is defined by the appended claims and equivalents thereof.

Claims (7)

1. The MIMO radar resource scheduling method based on the PSO optimization algorithm is characterized by comprising the following steps:

step 1: constructing an optimized model of resource scheduling in an MISO mode of the MIMO radar based on a radar task structure and a radar resource constraint condition;

step 2: solving the optimization model by utilizing a PSO optimization algorithm based on an entropy value;

and step 3: and outputting an optimal scheduling sequence according to the solution of the optimal model, and arranging the execution sequence of each task on the time axis according to the obtained optimal scheduling sequence.

2. The MIMO radar resource scheduling method based on the PSO optimization algorithm of claim 1, wherein the radar task structure in step 1 comprises three subtasks: a transmission period, a waiting period, and a reception period, the kth radar task is represented as:

T_k＝{P_k,t_ak/t_ek,t_xk,t_wk,t_rk,P_tk,t_dwk,w_k,t_dk,Δt_k} (1)，

wherein, P_kIs priority, t_akIs the request time, t_ekIs execution time, t_xkIs the emission period, t_wkIs a waiting period, t_rkIs a reception period, t_dwkIs the dwell time, w_kIs a time window, t_dkIs a cut-off period, Δ t_kFor two times of same speciesRequest intervals of adjacent tasks;

and a dwell time t_dwkSatisfies the following conditions:

t_dwk＝t_xk+t_wk+t_rk (2)，

end period t_dkSatisfies the following conditions:

t_dk＝t_ak+w_k (3)，

request interval Δ t_kSatisfies the following conditions:

t_ak＝t_e(k-1)+Δt_k (4)。

3. the PSO optimization algorithm-based MIMO radar resource scheduling method of claim 2, wherein the resource scheduling optimization model of step 1 comprises an objective function and a resource constraint condition, and the objective function of the resource scheduling in MISO mode of MIMO radar is:

the resource constraint conditions are as follows:

s.t.

t_dwk＝t_xk+t_wk+t_rk (19)，

t_dk＝t_ak+w_k (20)，

t_end＝t_start+t_SI (21)，

max(t_ak-w_k,t_start)≤λ_kt_ek≤min(t_dk,t_end-t_dwk) (22)，

ξ_iλ_it_ei≥ξ_kλ_k(t_ek+t_xk+t_wk+t_rk) (23)，

i,k＝1,2,...N,i≠k (30)，

t_ai+w_i≥t_end (35)，

t_ai+w_i＜t_end (36)，

wherein, t_startAnd t_endRespectively the start and end times, t, of the SI_SIIs the SI time length, the SI is the minimum time unit of radar task scheduling,

is a power threshold, P_τ(t) is the power consumption value of the radar at the time t, and p (x) is the instantaneous power consumption of the radar; τ is a backoff parameter.

4. The method for scheduling MIMO radar resources based on PSO optimization algorithm of claim 1, wherein the PSO optimization algorithm based on entropy in step 2 comprises:

step 21: initializing parameters, generating a chaotic sequence by adopting a Logistic equation based on the initialized parameters, optimizing an initialized population, and generating the chaotic sequence according to the formula:

η(q+1)＝μη(q)[1-η(q)] (46)，

wherein eta (q) is a result of iteration of a chaos variable eta for q times, and eta belongs to [0,1 ]; mu is a control parameter of the chaotic state, and mu belongs to [0,4 ];

and μ ═ 4, and,

step 22: adopting a heuristic interleaving algorithm to interleave and schedule tasks of different types;

step 23: expressing the diversity of the population genes by using an entropy value, and performing iterative optimization by using a PSO algorithm;

step 24: in the iterative optimization process, the cross probability P in the GA algorithm is measured by using the entropy value_cAnd the mutation probability P_mOptimizing and selecting the ones with poorer adaptive values when performing the crossover operation

The particles are used as parents and randomly selected in mutation operation

The individual particles serve as parents, and the population diversity is improved through the crossing and mutation operations;

step 25: judging t is more than or equal to t_maxAnd if so, directly outputting the optimal scheduling sequence, and if not, turning to the step 22 to continue iteration.

5. The PSO optimization algorithm-based MIMO radar resource scheduling method of claim 4, wherein the heuristic interleaving algorithm of step 22 comprises the steps of:

step 221: setting N genes of the population to be arranged in ascending order, wherein the number of the arranged request tasks is N, and the time axis of the SI is [ t ]_start,t_end]The ith time slice occupied by the receive period of the scheduled task is [ t ]_rsi,t_rei]And i is equal to 1,2, …, m, m is less than or equal to n, and the time pointer of the end time of the nth task transmitting period which indicates the latest successful scheduling is t_xenThe power pointer indicating the power consumption after the end of the most recently successfully scheduled task is P_t0The rest N-N request tasks are respectively coded into tasks 0,1,2, … and N-N-1;

step 222: at t_e0When the task 0 is scheduled at any moment, time feasibility detection is respectively carried out on the transmitting period and the receiving period of the task 0, if the transmitting period and the receiving period both meet corresponding time constraints, energy feasibility detection is carried out on the task 0, and if the time feasibility detection and the energy feasibility detection both meet the requirements, the task 0 is carried out at t_e0The time can be successfully scheduled;

in particular, the amount of the solvent to be used,

the time feasibility test for the emission period is as follows:

when the transmission of task 0 expires equation (37), (38), or (39), then the time constraint is satisfied;

the time feasibility detection in the receiving period is as follows:

t_e0+t_x0+t_w0+t_r0≤t_end (40)，

when the receipt of task 0 expires, equation (40), then the time constraint is satisfied;

the energy feasibility test is as follows:

when task 0 satisfies equation (41), then the energy constraint is satisfied;

and when

When, task 0 is at t_e0The time can be successfully scheduled;

step 223: updating the time index to t_e0+t_x0Updating the power pointer P_t0Is P_testAnd updating the time slice occupied by the receiving period of the scheduled task to be t_rs0,t_re0]∪[t_rsi,t_rei](i ═ 1,2, …, m), thereby achieving interleaving of scheduled tasks.

6. The PSO optimization algorithm-based MIMO radar resource scheduling method of claim 4, wherein the specific operation of step 23 comprises:

step 231: the population diversity is represented by entropy values: setting the population base number to N_popEach particle individually comprises N genes, N_popThe set of jth gene in the individual is j, and the number of jth gene in j of ith particle is b_ijThen the probability of the gene in the population is:

P_ij＝b_ij/N_pop (48)，

the entropy of the gene is:

the diversity of the population can be represented by the mean entropy:

step 232: setting the inertia weight w in the PSO algorithm by the mean entropy of the genes:

in the formula, w_min、w_maxUpper and lower bounds of the inertial weight, respectively;

step 233: optimizing in a discrete domain by using a PSO algorithm: setting the minimum discrete time unit to Δ t_pThe velocity and position of each individual is updated using equations (43) and (45):

in the formula,

and

respectively the position and velocity vector, p, of the particle_best(t) the best solution found so far for each particle; g_best(t) is the optimal solution found so far for the population of particles; r is₁、r₂Is a random number between 0 and 1; c. C₁And c₂Is a cognitive parameter, and c₁＝c₂2, round (.) is the rounding operation.

7. The PSO optimization algorithm-based MIMO radar resource scheduling method of claim 4, wherein the optimizing the crossover and mutation probabilities by entropy in step 24 comprises:

optimizing the cross probability:

wherein, P_cmaxAnd P_cminThe upper and lower bounds of the cross probability are respectively;

and (3) mutation probability optimization:

wherein, P_mmaxAnd P_mminThe upper and lower bounds of the variation probability are respectively.

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