Real-time distributed radar network beam dwelling scheduling method based on pulse staggering

Abstract

The present application belongs to the field of radar system resource management, and particularly relates to a method for adaptive beam dwelling scheduling of a distributed radar networking system. The present application first extends the beam dwelling scheduling method based on a time pointer of a single radar to a distributed radar networking beam dwelling scheduling method, and determines the matching relationship between the radar and the task according to the time utilization of each radar to ensure that each radar has a very high time utilization. In addition, the present application introduces a pulse stagger analysis matrix to stagger the dwelling tasks with different pulse repetition periods and pulse repetition intervals, thereby greatly improving the time utilization. Finally, the present application introduces a time utilization threshold to accelerate the sliding speed of the time pointer vector, thereby reducing the calculation complexity of the method and ensuring the real-time performance of the present application, so that the present application can be applied to actual distributed radar networking beam dwelling scheduling.

Description

TECHNICAL FIELD

[0001] The present application belongs to the field of radar system resource management, and particularly relates to an adaptive beam dwelling scheduling method for distributed radar networking. BACKGROUND

[0002] Compared with single station radar, distributed radar networking has better detection, tracking, parameter estimation, interference suppression and anti-fading capability (see the document: Zhou Wen-hui. Phased array radar and networking tracking system resource management technology research[D]. National University of Defense Technology, 2004.). In order to maximize the performance of distributed radar networking, a high-efficiency real-time beam dwelling scheduling algorithm needs to be designed.

[0003] In recent years, the research on beam dwell scheduling mainly focuses on the beam dwell scheduling of single station radar. The literature (Lu J, Hu W, Yu W. Real-time task scheduling for multifunction phased array radar[J]. Journal of Electronics, 2006, 34(4): 732-736.) designs a time pointer-based phased array radar beam dwell scheduling method. This method introduces a time pointer in the scheduling analysis. At the time when the time pointer is at, the task with the highest overall priority is selected for execution. The resulting scheduling sequence can effectively meet the importance and urgency criteria of beam dwell scheduling. The literature (Zhang H, Xie J, Zong B, et al. Dynamic priority scheduling method for the air-defence phased array radar[J]. IET Radar Sonar&Navigation, 2017, 11(7): 1140-1146.) designs a dynamic priority-based beam dwell scheduling method for the beam dwell scheduling problem of air defense phased array radar. This algorithm combines the threat degree of the target and the deadline of the task in the design of dynamic priority, and also introduces a time pointer in the scheduling analysis process to improve the time utilization of the algorithm. The literature (Tan Q, Cheng T, Li X. Online adaptive dwell scheduling based on dynamic template for PAR[J]. Journal of Systems Engineering and Electronics, 2021, 32(5): 1119-1129.) introduces a dynamic template in the beam dwell scheduling of phased array radar, which realizes the interleaving of tasks with different pulse repetition periods and pulse repetition intervals, and further improves the time utilization of beam dwell scheduling. The literature (Cheng T, Li Z, Tan Q, et al. Real-time adaptive dwell scheduling for digital array radar based on virtual dynamic template[J], IEEE Transactions on Aerospace and Electronic Systems, 2022, 58(4): 3197-3208) extends the beam dwell scheduling method based on dynamic template to the beam dwell scheduling of digital array radar.A hybrid adaptively genetic algorithm for task scheduling problem in the phased array radar[J]. European Journal of Operational Research, 2019, 272(3): 868-878. proposed a phased array radar beam dwell scheduling algorithm based on hybrid adaptive genetic algorithm. An entropy-based PSO for DAR task scheduling problem[J]. Applied Soft Computing, 2018, 73: 862-873. used a hybrid particle swarm-based beam dwell scheduling algorithm to achieve beam dwell scheduling in digital array radar.

[0004] In the beam dwell scheduling of distributed radar network, in addition to the actual execution time of beam dwell task, the specific radar node that executes the beam dwell task is also needed to be determined. The earliest deadline first (EDF) algorithm used to solve the multi-pipeline scheduling problem is extended to the beam dwell scheduling of multi-channel radar in the literature (Shaghaghi M, Adve R S. Task selection and scheduling in multifunction multichannel radars [C]. IEEE Radar Conference, Seattle, USA, 2017: 0969-0974.), and a beam dwell scheduling method based on branch and bound (B&B) for multi-channel radar is also proposed. The literature (Shaghaghi M, Adve R S. Machine learning based cognitive radar resource management [C]. IEEE Radar Conference, Oklahoma City, USA, 2018: 1433-1438; Shaghaghi M, Adve R S, Ding Z. Multifunction cognitive radar task scheduling using monte carlo tree search and policy networks [J]. IET Radar Sonar & Navigation., vol. 12, no. 12, pp. 1437-1447, 2018; Xu L, Zhang T. Reinforcement learning based dynamic task scheduling for multifunction radar network [C], IEEE Radar Conference, Florence, Italy, 2020: 1-5.) respectively uses machine learning, Monte Carlo search tree and Q learning to realize the beam dwell scheduling of distributed system. The literature (Liu X, Zhang Q, Luo Y, et al. ISAR imaging task allocation for multi-target in radar network based on potential game [J]. IEEE Sensor Journal, 2019, 19(23): 11192-11204.) uses potential game to realize the ISAR imaging task allocation for multi-target in radar network.)A convex optimization based beam dwell scheduling method is adopted to realize the beam dwell in the distributed system considering the imaging task. The above beam dwell in the distributed system has achieved certain results, but there are still the following problems: (1) The above literature regards the dwell task as a non-preemptive task, and fails to fully utilize the waiting period of the dwell request; (2) The beam dwell scheduling algorithm using the heuristic method (see literature: Shaghaghi M, Adve R S. Task selection and scheduling in multifunction multichannel radars [C]. IEEE Radar Conference, Seattle, USA, 2017: 0969-0974.) in the above literature, although it has small computational complexity and real-time performance, the performance of the obtained scheduling sequence is poor, and it cannot meet the importance and urgency criteria of beam dwell scheduling, while the intelligent method (see literature: Shaghaghi M, Adve R S. Task selection and scheduling in multifunction multichannel radars [C]. IEEE Radar Conference, Seattle, USA, 2017: 0969-0974.; Shaghaghi M, Adve R S. Machine learning based cognitive radar resource management [C]. IEEE Radar Conference, Oklahoma City, USA, 2018: 1433-1438.; Shaghaghi M, Adve R S, Ding Z. Multifunction cognitive radar task scheduling using Monte Carlo tree search and policy networks [J]. IET Radar Sonar & Navigation., vol. 12, no. 12, pp. 1437-1447, 2018.; Xu L, Zhang T. Reinforcement learning based dynamic task scheduling for multifunction radar network [C], IEEE Radar Conference, Florence, Italy, 2020: 1-5.; Shaghaghi M, Adve R S.The scheduling method of the machine learning based cognitive radar resource management (C. IEEE Radar Conference, Oklahoma City, USA, 2018: 1433-1438.) is not real-time and cannot be applied to the actual beam dwell scheduling analysis.

[0005] Based on the above problems, the application provides a real-time distributed radar networking beam dwell scheduling method based on pulse interleaving. The application first extends the time pointer based beam dwell scheduling method of a single station radar to a distributed radar networking beam dwell scheduling method, and determines the matching relationship between the radar and the task according to the time utilization rate of each radar to ensure that each radar has a very high time utilization rate. In addition, the application introduces a pulse interleaving analysis matrix, so that the dwell tasks with different pulse repetition periods and pulse repetition intervals can be interleaved, greatly improving the time utilization rate. Finally, the application introduces a time utilization threshold to speed up the sliding speed of the time pointer vector, thereby reducing the computational complexity of the method. SUMMARY

[0006] The application provides a real-time distributed radar networking beam dwell scheduling method based on pulse interleaving, and has the characteristics that:

[0007] Suppose that there are N dwell tasks T = [T1, T2,..., T N ] to be scheduled on M phased array radars R = [R1, R2,..., R j ,..., R M ] in the current scheduling interval [t0, t0+t SI ], where t0 is the start time of the current scheduling interval, t SI is the length of the scheduling interval, and (t0+t i ) is the end time of the current scheduling interval. The dwell task model is T i ={W i dt i l i tx i tw i tr i pri i M i Pt i}, where W i is the working mode priority, dt i is the expected execution time, l i is the time window, tx i is the transmission period, tw i is the waiting period, tri For the receiving period, pri i M is the pulse repetition period. i Pt is the number of pulse repetition periods. i The transmit power is used. The real-time distributed radar networking beam dwell scheduling method based on pulse interleaving includes the following steps:

[0008] Step 1: Initialize the time pointer vector tp = [tp1, tp2, ..., tp] for each radar. j ,...,tp M [t0, t0, ..., t0], initialize the time tl = [tl1, tl2, ..., tl] when the last task of each radar is completed. j ,...,tl M [t0, t0, ..., t0], initializing the time interval Δt to the minimum launch period in the requested scheduling task, and initializing the time matrix. Energy Matrix in The element E corresponding to the j-th row and k-th column in the energy matrix jk The initialization method is as follows:

[0009]

[0010] in, Let τ be the energy at the start of the j-th radar scheduling interval, and τ be the backoff parameter.

[0011] Step 2: Select tasks from the task request queue T that satisfy dt i +l i Tasks with a value less than min(tp) are removed from the task deletion queue.

[0012] Step 3: Select the task request queue T that satisfies max(tp)≥dt i -l i Given all tasks, assuming there are X tasks selected, if X > 0, calculate the priority of each task using the following formula: sw i :

[0013]

[0014] Among them, Xd i For task request T i (1≤i≤X) is the sequence number of X tasks, arranged in descending order of their deadlines. i To sort the X tasks by their work priority from smallest to largest, sort these X tasks by their overall priority from largest to smallest, initialize itp=1 and go to step 4; if X=0, go to step 11.

[0015] Step 4: Retrieve the itp-th task T from the sorted task queue. itp Select the ones that can be used for scheduling T itp radar set R itp R itp Radar R in j The following requirements should be met: dt i -l i ≤tp j ≤dt i +l i ∩tp j +dw i ≤t0+t SI ,R j ∈R itp (3)

[0016] Among them, dw i =pri i ·(M i -1)+tx i +tw i +tr i Duration of stay for a stationed mission;

[0017] Step 5: If R itp If R is not empty, proceed to step 6; if R is not empty, proceed to step 6. itp If R is empty and itp < X, then itp = itp + 1, and return to step 4; if R is empty... itp If it is empty and itp = X, then proceed to step 11;

[0018] Step 6: Calculate R according to equation (4) itp The time utilization rate (tu) of the medium radar between the time pointer and the latest mission completion time. itp , among which, tu j For tu itp The elements in and They represent tp respectively j and tl j At the position of the j-th row of matrix S, S jk This represents the element in the j-th row and k-th column of matrix S;

[0019] Step 7: Analyze T itp Can it be dispatched to radar R? j* ∈R itp Above; where j* is tu itp The index of the smallest element in the middle:

[0020] j*=argmin(tu itp(7)

[0021] Calculate according to the following formula The corresponding time change vector and energy change vector

[0022]

[0023]

[0024]

[0025] Step 8: Determine T based on the following system of inequalities. itp Can it be scheduled onto a selected radar?

[0026]

[0027] If the condition is met, proceed to step 9; otherwise, proceed to step 11.

[0028] Step 9: Place T itp Put in In the task execution queue, and put T itp Remove from the task request queue, update S and E according to equation (12), and update tl according to equation (13). j ;

[0029]

[0030]

[0031] Step 10: Recalculate the updated value according to equation (4). Update according to the following formula Proceed directly to step 12:

[0032]

[0033] Where tu th This is a threshold for time utilization.

[0034] Step 11: Update min(tp) = min(tp) + Δt. If radar j has tp after the update... j >tl j , then tl j =tp j ;

[0035] Step 12: If T is not empty and min(tp) < t0 + t SI If the result is positive, return to step 2; otherwise, the analysis of this scheduling interval ends.

[0036] Inventive Principles

[0037] Radar beam dwell scheduling needs to follow two principles: importance and urgency. The importance principle means that the radar system should schedule as many high-priority tasks as possible, while the urgency principle means that tasks with earlier deadlines should be executed as early as possible. Based on these two principles of dwell scheduling, the following scheduling reward function is constructed for each beam dwell task:

[0038] G i (dt i ,l i W i ,t0)=g1(W i )g2(dt i ,l i ,t0) (15)

[0039] in,

[0040]

[0041] Because g1(W i The value increases with the priority of the task's working method, thus reflecting the importance criterion of scheduling; g2(dt) i ,l i In the interval [t0, t0+t), c1 is a positive constant. Because it increases as the task deadline decreases, this term reflects the scheduling urgency criterion. Assume that in the current scheduling interval [t0, t0+t...], c1 is a positive constant. SI There are N resident tasks T = [T1, T2, ..., T] N The application is made for M phased array radars R = [R1, R2, ..., R...] j ,...,R M Based on the above scheduling revenue function and the constraints in the distributed system scheduling problem, the mathematical model for the distributed system beam dwell scheduling problem can be established as follows:

[0042]

[0043] st.

[0044]

[0045] at i ∈[max(t0,dt i -l i ),min(dt i +l i ,t0+t SI -pri i ×(M i -1)-(tx i +twi +tr i ))],i = 1,2,...,N1

[0046]

[0047]

[0048]

[0049]

[0050] E p (t)≤E th ,t∈[t0,t0+t SI ),p = 1,...M

[0051] dt u +l u ≥t0+t SI , u = 1,2,...,N2

[0052] dt v +l v <t0+t SI , v = 1,2,...,N3 (17)

[0053] where at i is the actual execution time of the actual execution task, represents the number of actual execution tasks on radar R p , N2 and N3 are the number of delayed tasks and the number of deleted tasks respectively, and N1 is the total of the number of all actual execution tasks, i.e. N2 and N3 should satisfy the first constraint condition. The second constraint condition indicates that all scheduled tasks must be executed within their executable time range. The third, fourth and fifth constraint conditions respectively indicate that the transmission period of different resident tasks on the same radar cannot coincide, the transmission period and the receiving period cannot coincide, and the receiving period and the receiving period cannot coincide. The sixth inequality represents the energy constraint condition, where E p (t) is the energy of radar R p at time t. The seventh and eighth inequalities indicate the conditions that the delayed and deleted tasks should satisfy. The above problem is a typical NP-hard problem.

[0054] To solve the problem, the application designs a real-time distributed radar networking beam dwell scheduling method based on pulse interleaving. To ensure that the scheduling sequence obtained by the application can meet the importance criterion of beam dwell scheduling, the application selects the application scheduling dwell task with the maximum comprehensive priority at the current time by introducing a time pointer vector in steps 3 and 4 for subsequent dwell scheduling analysis. The essence of pulse interleaving is to make full use of the remaining available resources on the time axis occupied by the scheduled tasks, so the application introduces a time utilization rate and uses this indicator to select a radar node for a high comprehensive priority task, as shown in step 6, wherein the time utilization rate is defined as shown in equation (4). To perform online interleaving analysis, the application introduces a time slot occupation matrix S and an energy consumption matrix E to represent the time and energy resource usage of the distributed system. If scheduling a task causes a time slot to be preempted, that is, the element in S exceeds 1, it is considered that the time resource constraint is not met in interleaving, and at the same time, if scheduling a task causes the element in E to exceed the threshold, it is considered that the energy resource constraint is not met in interleaving, as shown in step 8. To effectively improve the execution efficiency of the algorithm, consider that for the radar nodes that have been fully utilized, slide the time pointer by a larger step. The application introduces a time utilization threshold tu th When the time utilization rate of the radar node exceeds the time utilization threshold, it is considered that the time resource of the node has been fully utilized, and the time pointer is slid to the latest task execution end time, as shown in step 10. BRIEF DESCRIPTION OF DRAWINGS

[0055] Figure 1 TDR comparison of three methods

[0056] Figure 2 HVR comparison of three methods

[0057] Figure 3 TUR comparison of three methods

[0058] Figure 4 Runtime comparison of three methods DETAILED DESCRIPTION

[0059] In the simulation scenario, five kinds of tasks, i.e., precision tracking, ordinary tracking, horizon search, space search and verification, are considered, wherein the horizon search task has three areas to search, the space search task also has three areas to search, and the ratio of the number of precision tracking targets to the number of ordinary task targets is 1:4. The radar task parameters are shown in Table 1. It is assumed that there are three phased array radars in the distributed radar networking system, and each radar can execute all the dwell tasks. The beam dwell scheduling of the distributed radar networking system is realized by using the application, the simulation time is 12s, the scheduling interval time is set to 50ms, the energy threshold E th is set to 10J, and the backoff parameter τ is 200ms.

[0060] Table 1. Radar beam dwell task parameter table

[0061]

[0062] To comprehensively evaluate the performance of the present application, this section uses the task drop ratio (TDR), hit value ratio (HVR), time utilization ratio (TUR), and running time as performance evaluation indicators. The above indicators are defined as follows:

[0063] The task drop ratio (TDR) is the ratio of the number of lost tasks to the number of scheduled tasks within the simulation duration:

[0064] TDR = N drop / N all (18)

[0065] where N drop represents the number of lost tasks, and N all represents the number of scheduled tasks.

[0066] The hit value ratio (HVR) is the ratio of the sum of the work mode priorities of the actual executed tasks to the sum of the work mode priorities of the scheduled tasks within the simulation duration:

[0067]

[0068] where N exe represents the number of actual executed tasks. This indicator is used to reflect the proportion of high-priority tasks that are successfully scheduled.

[0069] The time utilization ratio (TUR) is defined as the ratio of the sum of the actual execution task transmission and reception periods to the product of the total simulation duration and the number of radar nodes:

[0070]

[0071] where t total is the total simulation duration, and M is the total number of radar nodes in the distributed networking system.

[0072] The real-time distributed radar network beam dwelling scheduling method based on pulse interleaving (referred to as the invention method in simulation) is adopted, and the performance is compared with method A and method B, wherein method A is a network radar beam dwelling scheduling algorithm based on the earliest deadline first algorithm (see the literature: Shaghaghi M, Adve R S. Task selection and scheduling in multifunction multichannel radars [C]. IEEE Radar Conference, Seattle, USA, 2017: 0969-0974.), and method B is an algorithm extended to network radar beam dwelling scheduling based on the time pointer-based beam dwelling scheduling algorithm (see the literature: Lu Jianbin, Hu Weidong, Yu Wenxian. Real-time task scheduling of multifunction phased array radar [J]. Electronics Letters, 2006, 34(4): 732-736.), which does not contain pulse interleaving analysis. The simulation platform is MATLAB R2019a, the computer processor is Core i7-10700, and the memory is 16G. Figures 1 to 4 The statistical results of 100 Monte Carlo under different indicators.

[0073] Figure 1 The task loss rate curve is shown. When the number of targets is 10, method A begins to have obvious task loss, because the earliest deadline first algorithm does not introduce a time pointer or pulse interleaving technology, so that the time resource cannot be fully utilized. When the number of targets is 60, method B has task loss. Because method B introduces a time pointer in the scheduling analysis process, it ensures that there is no time gap in the actual execution queue of the task, and improves the utilization rate of time resources, so that the task loss rate curve is lower than that of method A. But method B cannot fully utilize the waiting period of the dwelling task because it does not introduce pulse interleaving analysis. The invention method begins to lose when the number of targets is 120, and has the lowest task loss rate. On the one hand, the invention first introduces a time pointer vector and a dynamic time utilization degree to ensure that the time resources of each radar node can be utilized as much as possible; on the other hand, the invention introduces pulse interleaving analysis so that the dwelling tasks with different pulse repetition periods and pulse repetition intervals can be interleaved, which makes the waiting period of the dwelling task available, and the time resource utilization degree of the network system is further improved.

[0074] Figure 2 In order to realize the value rate curve, the curve reflects whether the tasks with higher priority of working mode can be executed as much as possible, and the curve trend is opposite to the loss rate curve. It can be seen that the realization value rate of the method is greatly improved compared with method A and method B.

[0075] Figure 3The time utilization rate curve is obtained. When the number of targets is small, the time utilization rate of the method linearly increases with the increase of the number of targets, when the number of targets reaches about 110, the networking system reaches a saturation state, and the curve trend tends to be stable. Due to the introduction of the time pointer vector, the time utilization rate of method B is higher than that of method A, and due to the introduction of the pulse interleaving technology, the time utilization rate of the method is higher than that of method B.

[0076] Figure 4 The average running time of the three methods in a scheduling interval is obtained. It can be seen that method A has the lowest average running time, and method B introduces a time pointer in the resident scheduling analysis, which improves the complexity of the algorithm. The present application further introduces a pulse interleaving analysis process compared with method B, which further improves the complexity of the algorithm. However, the three methods can complete the resident scheduling analysis in a scheduling interval (50 ms) to obtain the actual execution tasks in the present scheduling interval. Therefore, the three methods can realize real-time scheduling.

[0077] In summary, compared with the networking radar beam resident scheduling algorithm based on the earliest deadline priority algorithm and the time pointer-based networking radar beam resident scheduling algorithm without introducing the pulse interleaving analysis, the radar networking beam resident scheduling method proposed in the present application has the lowest task loss rate, the highest implementation value rate and time utilization rate, and has real-time performance, and can be applied to actual distributed networking radar systems.

Claims

1. A real-time distributed radar networking beam dwelling scheduling method based on pulse interleaving, characterized by: Suppose that there are N resident tasks T = [T1, T2,..., T N ] to be applied on M phased array radars R = [R1, R2,..., R j ,...,R M ] in the current scheduling interval [t0, t0+t SI ], where t0 is the starting time of the current scheduling interval, t SI is the duration of the scheduling interval, (t0+t i ) is the end time of the current scheduling interval, the resident task model is T i ={W i dt i l i tx i tw i tr i pri i M i Pt i}, where W i is the working mode priority, dt i is the expected execution time, l i is the time window, tx i is the transmission period, tw i is the waiting period, tr i is the receiving period, pri i is the pulse repetition period, M i is the number of pulse repetition periods, and Pt j is the transmission power, the beam resident scheduling method of the real-time distributed radar networking system based on pulse interleaving comprises the following steps: Step 1: Initialize the time pointer vector tp = [tp1, tp2, ..., tp] for each radar. j ,...,tp M [t0, t0, ..., t0], initialize the time tl = [tl1, tl2, ..., tl] when the last task of each radar is completed. j ,...,tl M [t0, t0, ..., t0], initializing the time interval Δt to the minimum launch period in the requested scheduling task, and initializing the time matrix. Energy Matrix in The element E corresponding to the j-th row and k-th column in the energy matrix jk The initialization method is as follows: wherein, is the energy at the start of the jth radar scheduling interval, and τ is a backoff parameter. Step 2: Select the task in the task request queue T that satisfies dt i + i <min(tp) and remove them from T and store them in the task removal queue; Step 3: Select a task from the task request queue T that satisfies max(tp) > dt i -l i of all tasks, assuming there are X selected tasks, if X > 0, calculate the priority sw of each task according to the following formula i : Xd i T is a task request i In the X tasks, the serial number arranged from large to small according to the deadline, Xp i In the X tasks, the serial number arranged from small to large according to the work mode priority, sort the X tasks from large to small according to the comprehensive priority, initialize itp = 1 and go to step 4; if X = 0, go to step 11; Step 4: Take the itp-th task T in the ordered task queue itp , select a radar set R itp available for scheduling T itp , the radar R itp in R j should meet the following requirements: dt itp -l itp ≤tp j ≤dt itp +l itp ∩tp j +dw itp ≤t0+t SI ,R j ∈R itp (3) where, dt itp and l itp are the expected execution time and time window of task T itp , respectively, dw itp =pri itp ·(M itp -1)+tx itp +tw itp +tr itp is the residence time of the resident task T itp , pri itp , M itp , tx itp , tw itp , tr itp are the pulse repetition period, the number of pulse repetition periods, the transmission period, the waiting period and the receiving period of task T itp , respectively. Step 5: If R itp is not empty, go to Step 6; if R itp is empty and itp < X, then itp = itp + 1 and return to Step 4; if R itp is empty and itp = X, go to Step 11. Step 6: Calculate R from (4) itp The time utilization of the radar between the time pointer to the end of the latest task execution time tu itp where tu j is the time utilization of the radar between the time pointer to the end of the latest task execution time tu itp is the element in tu and respectively represent tp j and tl j on the jth row of the matrix S, S jk represents the element in the jth row and the kth column of the matrix S; Step 7: Analysis T itp Can be scheduled to radar R j* ∈R itp Upper; where j* is the index of the minimum element in tu itp The index of the minimum element in j = argmin(tu itp R is calculated as follows j* the corresponding time change vector ΔS j* and the energy change vector ΔE j* ; Step 8: Determine T according to the following set of inequalities itp whether it can be scheduled on the selected radar: if the condition is met, go to step 9, otherwise go to step 11; Step 9: Put T itp into the task execution queue of R j* and delete T itp from the task request queue, update S and E according to (12) and update tl j according to (13). Step 10: Recalculate updated (4) as Update (4) according to and go directly to Step 12: tu < tu max th is a time utilization degree threshold value; Step 11: Update min(tp) = min(tp) + At, if after the update there exists a radar j with tp j > t j l j = tp j ; Step 12: If T is not empty and min(tp) < t0+ t SI then go to step 2, otherwise the current scheduling interval analysis is finished.

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