Beam dwell scheduling method for simultaneous multi-beam radar based on polarization-adaptive array element selection

Abstract

The present invention belongs to the field of radar system resource management, and in particular to a novel real-time adaptive resident scheduling method for phased array radar. The present invention first constructs a comprehensive priority by combining the task working mode priority with the deadline, and sorts the executable tasks from large to small according to the comprehensive priority. Subsequently, the formula for the average power requirement of task reception is derived according to the polarization characteristics of the array elements. An array element combination is selected for the executable task according to the task sequence and power requirement, and the remaining array elements can be used to execute the next task at the same time. Thus, the method can execute multiple tasks at the same time and realize simultaneous multi-beam resident scheduling. Simulation results show that compared with the existing method, this method can greatly reduce the task loss rate, improve the time utilization of the system, and has real-time performance, and can be applied to actual radar systems.

Description

Technical Field

[0001] The invention belongs to the field of radar system resource management, and in particular relates to a method for adaptive resident scheduling of a phased array radar. Background Art

[0002] In an increasingly complex war environment, phased array radar (PAR) is widely used due to its advantages such as multi-function and multiple working modes. This is largely dependent on the simultaneous multi-beam capability of phased array radar. Phased array radar can transmit multiple independent beams at the same time, so it can perform tasks such as simultaneous multi-target monitoring, tracking, positioning, and imaging. There are three types of multi-beam implementation methods at present. One is to use the beam agility characteristics of phased array radar to send beams with different directions within the pulse repetition period to approximately achieve simultaneous multi-beam (Chen J, Tian Z, Wang L, et al. Adaptive simultaneous multi-beam dwell scheduling algorithm for multifunction phased array radars [J]. Journal of Information & Computational Science, 2011, 8 (14): 3051-3061.). The second is to achieve multi-beam forming by designing the weighted coefficients of the radiation signals of each array element. The literature (Wei Fa, Yang Minglei, He Xiaojing, Zhou Dingsen, Chen Boxiao. Simultaneous multi-beam forming method of planar array based on improved particle swarm algorithm [J]. Systems Engineering and Electronics, 2022, 44 (06): 1789-1797.) proposed a simultaneous multi-beam forming method of planar array based on improved particle swarm algorithm, and studied the feasible method of simultaneous multi-beam forming of large phased array planar array with a large number of array elements. The third is to use the phased array aperture to divide it into several sub-arrays, each of which can emit a beam separately, thereby achieving simultaneous multi-beam (Xue G, Du Z, Wei W, et al. Multi-beam dwell adaptive scheduling algorithm for helicopter-borne radar [C] Information Technology & Artificial Intelligence Conference. 2014: 401-404.). In order to give full play to the effectiveness of the simultaneous multi-beam radar system, an effective beam dwell scheduling method needs to be designed.

[0003] In the early stage, fixed template, multi-template and partial template scheduling strategies were usually used to design the beam dwell scheduling strategy of radar system. However, the template method lacks the ability to adaptively match the actual task load. Therefore, the adaptive beam dwell scheduling algorithm has been widely studied. The literature (Lu Jianbin, Hu Weidong, Yu Wenxian. Research on real-time task scheduling of multifunctional phased array radar [J]. Journal of Electronics, 2006, 34 (4): 732-736.) proposed an adaptive beam dwell scheduling algorithm, in which the concept of time pointer was introduced to enable the task priority to change dynamically during the scheduling process. The priority comprehensively considers the two parameters of the task's working mode priority and deadline. 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.) comprehensively considers the threat level and deadline of the target, and designs a dynamic priority based on this. The literature (Mir HS, Guitouni A. Variable Dwell Time Task Scheduling for Multifunction Radar [J]. IEEE Transactions on Automation Science and Engineering, 2014, 11 (2): 463-472.) models the task dwell time as a variable, which allows the task dwell time to have a certain degree of flexibility, thereby enhancing the utilization of the radar timeline. The literature (Qu Z, Ding Z, Moo P. Dual-Side Scheduling for Radar Resource Management [C] 21st International Radar Symposium (IRS), 2020: 260-263) considers the expected execution time criterion and proposes a two-sided scheduling method, setting a separation point in a scheduling interval, dividing a scheduling interval into two sides, and scheduling tasks from the separation point to both sides of the scheduling interval. However, the above literature only considers the single-beam dwell scheduling problem, and the array element utilization is not flexible, so the task loss rate increases significantly when the total number of tasks increases.

[0004] In order to solve the above problems, the literature (Chen J, Tian Z, Wang L, et al. Adaptive simultaneous multi-beam dwell scheduling algorithm for multifunction phased array radars [J]. Journal of Information & Computational Science, 2011, 8 (14): 3051-3061.) calculates the maximum beam overlap number of the phased array radar system and introduces a virtual dwell timeline method to achieve multi-beam dwell scheduling. However, this method does not essentially achieve the simultaneous transmission of multiple beams, but only uses the pulse overlap technology to transmit beams in different directions within a pulse repetition period, thereby improving the time utilization of the system. The literature (Xue G, Du Z, Wei W, et al. Multi-beam dwell adaptive scheduling algorithm for helicopter-borne radar [C] Information Technology & Artificial Intelligence Conference. 2014: 401-404.) uses the phased array aperture to divide into several sub-arrays, and selects different radar working modes according to different target distances. Different working modes occupy different sub-array resources, and the remaining resources can be used to perform other tasks, thereby realizing simultaneous multi-beam dwell scheduling.

[0005] In the above-mentioned simultaneous multi-beam dwell scheduling algorithm, the polarization characteristics of the array elements are not considered. However, with the development needs of airborne detection platforms, conformal arrays have emerged. The array elements that fit the surface of the carrier are affected by the array position, resulting in different array elements having different polarization characteristics in the same coordinate system.

[0006] In view of the above problems, the present invention proposes a beam dwell scheduling method for simultaneous multi-beam radar based on polarization characteristic adaptive array element selection. This method uses the method proposed in the literature (Sun Shili, Liu Shuai, Jin Ming. Conformal array modeling method based on Euler rotation and polarization projection [J]. Signal Processing, 2021, 37(08): 1430-1440.) to obtain the local directional pattern representation of the array element by Euler rotation, and then obtain the polarization vector by polarization projection process in the global rectangular coordinate system, obtain the polarization vector of each array element in the global rectangular coordinate system, and allocate different array elements to transmit beams for different types of tasks according to the mission combat performance requirements, thereby realizing simultaneous multi-beam. Subsequently, in the simultaneous multi-beam dwell scheduling process, the idea of ​​the beam dwell scheduling method based on the time pointer is adopted. When sliding the time pointer, the task with the largest dwell time in the currently scheduled task is used as the sliding step size for updating the time pointer. The simulation results show that compared with the existing methods, this method effectively improves the scheduling performance of the simultaneous multi-beam radar system. Summary of the invention

[0007] The present invention proposes a beam dwell scheduling method for a simultaneous multi-beam radar based on polarization characteristic adaptive array element selection. The polarization characteristics of the array element are briefly described below:

[0008] After considering polarization, the transmission characteristics of the i-th array element can be expressed by the vector Describe (1≤i≤N total ), where θ is the pitch angle, is the azimuth, N total is the total number of array elements, is the array element i The projection of the radiation characteristics in the x direction, is the array element i The projection of the radiation characteristics in the y direction, is the array element i The projection of the radiation characteristics in the z direction.

[0009] Assume that in the current scheduling interval t0,t end There are N resident tasks T = T1, T2, ..., T N Apply for scheduling, where t0 is the start time of the current scheduling interval, t end is the end time of the current scheduling interval, t end -t0 is the duration of this scheduling interval. The resident task model is Among them, rt i is the expected execution time, st i is the actual execution time, l i is the time window, p i is the working mode priority, Δti For the length of stay, is the average power demand received by the mission, pt i is the signal transmission power, The beam dwell scheduling method of a simultaneous multi-beam radar system based on polarization characteristic adaptive array element selection includes the following steps:

[0010] Step 1: Initialize the time pointer tp, setting tp=t0, i=0.

[0011] Step 2: Select the tasks in the task request queue T that satisfy rt+l<tp, and record the number of these tasks as n i , delete them from the task request queue, and then store them in the task deletion queue, i = i + n i , let M = N total , N total is the total number of array elements.

[0012] Step 3: In the task request queue, assume that there are X tasks that satisfy tp ≥ rt-l. If X>0, calculate the priority sw of each task according to formula (1): i , where Xd i Request T for the task i (1≤i≤X) is the number of tasks in descending order of deadline, Xp i It is the sequence number of X tasks arranged from small to large according to the priority of work mode.

[0013]

[0014] Sort these X tasks by their comprehensive priority from highest to lowest, and set itp = 1. If X = 0, update the time pointer tp = tp + Δtp min , where Δtp min is the minimum sliding step of the time pointer. After updating, if tp≥t end , then the scheduling interval analysis ends; otherwise, return to step 2.

[0015] Step 4: Take the itpth task T in the sorted task queue itp .

[0016] Step 5: If tp+Δt itp >t end , then the analysis of this scheduling interval ends, Δt itp T itp Otherwise, let zy_use i is empty, m=1, and execute the next step.

[0017] Step 6: According to T itpThe direction parameter of the task T can be found in each polarization direction of the array element by formula (2). itp The direction that best matches the target direction θ min With θ max are the minimum and maximum values ​​of the pitch angle, and are the minimum and maximum values ​​of the azimuth angle, Δθ, is the dispersion of the elevation and azimuth angles.

[0018]

[0019] So for task T itp , M array elements in The polarization characteristics of the direction form a matrix as shown in formula (3).

[0020]

[0021] Step 7: Calculate the M array elements according to equation (4) The square sum of each component of the polarization characteristic of the direction is calculated and sorted from large to small, and the array element number sorted in this way is stored in zy_num.

[0022]

[0023] Step 8: Select the first m array elements in zy_num to calculate the power value, recorded as P cal .

[0024] Step 9: If P cal ≥P des , then M=Mm, and jump to step 11, otherwise m=m+1, and go to step 10.

[0025] Step 10: If m>M, jump to step 13, otherwise, return to step 8.

[0026] Step 11: T itp Put it into the task execution queue and put T itp Delete from the task request queue, set i=i+1, and store the m array element numbers used in zy_use i , represents the array element sequence number set used by task i. Delete these array elements in zy and set T itp The residence time is stored in t_store, itp=itp+1.

[0027] Step 12: If itp≤X and M>0, return to step 4, otherwise go to step 13.

[0028] Step 13: After the scheduling analysis at time tp is completed, the time pointer tp=tp+max(t_store) is updated.

[0029] Step 14: If i=N, the analysis of this scheduling interval ends, otherwise jump to step 2.

[0030] Principle of the Invention

[0031] The radar beam dwell scheduling process needs to follow two criteria, including the importance criterion and the urgency criterion. According to these two scheduling criteria, the following scheduling benefit function is constructed for each beam dwell scheduling task:

[0032] G i (rt i ,l i ,p i ,t0,t end )=g1(p i )g2(rt i ,l i ,t0,t end ) (5)

[0033] in,

[0034]

[0035] Because g1(p i ) increases with the priority of the task working mode, so this item reflects the importance of scheduling; g2(rt i ,l i ,t0,t end ) where c1 is a positive constant, because it increases as the deadline of the task decreases, so this item reflects the urgency criterion of scheduling. Although the traditional time pointer-based analysis method can effectively solve the above problem model, due to the single beam working mode, the algorithm only selects one task to execute at each analysis moment. The present invention considers adaptively selecting array elements based on polarization characteristics to realize simultaneous multi-beam, and combines it with the beam residence scheduling method based on time pointer. Taking into account the objective function and constraints in the simultaneous multi-beam residence scheduling problem, the mathematical model of the beam residence scheduling problem is established as follows:

[0036]

[0037] Among them, N1, N2 and N3 are the number of scheduled tasks, the number of delayed tasks and the number of deleted tasks respectively. Obviously, N=N1+N2+N3. i is the number of array elements used for the task, X is the total number of executable tasks at the current moment, δ iis a Boolean variable, which is 1 if task i is executed, otherwise 0. In the optimization model, the second and third inequalities reflect the conditions that delayed tasks and deleted tasks should meet. The fourth and fifth inequalities indicate that the total number of array elements used by tasks executed at the same time does not exceed the total number of array elements in the system and array elements cannot be reused.

[0038] The transmitted signal is represented as s(t). If the unit vectors in all directions are introduced and Then for The target is at , ignoring the influence of noise, and after using the desired signal array steering vector to complement the phase, the signal emitted by array element i is:

[0039]

[0040] arrive The signal at the target is:

[0041]

[0042] The signal received by each array element can be expressed as and the inner product of their respective polarization characteristic vectors. Therefore, the received signal of array element j after phase complementation can be expressed as:

[0043]

[0044] in, Substituting (9) into (10), we obtain:

[0045]

[0046] Each array element receiving channel will be affected by the receiving noise when receiving the target echo signal. Therefore, the actual receiving signal of array element j can be expressed as:

[0047]

[0048] Among them, v j (t) is the receiving noise of array element j, assuming it is Gaussian white noise with a power spectrum density of N0. The received signal is matched filtered to obtain:

[0049]

[0050] make

[0051]

[0052]

[0053] Among them, E s is the energy of the transmitted signal s(t), substituting equation (11) into (13) to obtain:

[0054]

[0055] Assuming that the receiving array is the same as the transmitting array, y j Represented as y i , the receiving beam form is:

[0056]

[0057] v i The power is:

[0058]

[0059] but The power is:

[0060]

[0061] Combined with the above process, the transmitted signal is After being scattered by the target, the receiving array receives the echo. Considering factors such as path attenuation during the propagation process, the received signal-to-noise ratio can be expressed as:

[0062]

[0063] Where r is the target distance, σ is the target RCS, λ is the signal wavelength, and E s =p t τ, p t is the transmit power of each array element, τ is the transmit signal pulse width, τB n ≈1, B n is the bandwidth, N0=kT0F n , k is the Boltzmann constant, T0 is the ambient temperature, F n is the receiver noise coefficient. Equation (20) can be written as:

[0064]

[0065] Through the above derivation, we can get the signal-to-noise ratio calculation formula that takes into account the polarization characteristics of the array element. According to the signal-to-noise ratio requirement of the task, its average power requirement is obtained. The signal-to-noise ratio requirement is expressed as SNR des , through formula (21), we can get the required average receiving power for the target at distance r and RCS σ:

[0066]

[0067] In step 1, it is assumed that there are N totalarray elements, according to their polarization characteristics, at the current execution time, multiple different array element combinations can obtain simultaneous multi-beams. When scheduling, the importance criterion and the urgency criterion require that tasks with high working mode priority and tasks with early deadlines should be executed as much as possible. In step 3, equation (1) reflects the above two criteria. In step 6, first find the polarization characteristic vectors of all available array elements in the task direction to form a set zy. According to equation (22), the key to determining the power value is In order to reduce the computational complexity and improve the execution efficiency of the system, a heuristic method is used to replace the exhaustive method. The exhaustive method is to traverse the optional array elements for each selection, calculate according to formula (22), and select the best one from them. In step 7, the heuristic method is used to select the array element. The array element is calculated in The sum of the squares of the polarization characteristics of the direction is sorted from large to small, and the array element numbers sorted in this way are stored in zy_num. The array elements are selected in zy_num in turn until the expected power of the task is met. Step 11 shows that if the executable tasks at the current moment have not been analyzed and there are still array elements left, then the array element combination is selected for the next task. At the current tp moment, the residence time of all tasks placed in the execution queue is stored in t_store in step 12, and the maximum value among them is used as the sliding step size for updating the time pointer. Finally, the final scheduling sequence and the array element combination results selected for the scheduling task are obtained. BRIEF DESCRIPTION OF THE DRAWINGS

[0068] Figure 1 This is a schematic diagram of simultaneous multi-beam dwell scheduling.

[0069] Figure 2 It is the array element arrangement model

[0070] Figure 3 There are three methods of TDR

[0071] Figure 4 There are three methods of TUR

[0072] Figure 5 There are three methods of HVR

[0073] Figure 6 is the running time of the three methods

[0074] Figure 7 Comparison of the number of array elements selected by different methods DETAILED DESCRIPTION

[0075] Four tasks are considered in the simulation scenario: precision tracking, general tracking, horizon search, and airspace search. The simulation duration is 12s, the scheduling interval is set to 50ms, the ratio of the number of precision tracking targets to the number of general task targets is 1:4, and the time pointer sliding step Δtp minis 1. The radar mission parameters are shown in Table 1.

[0076] Table 1. Radar beam dwell mission parameters

[0077]

[0078] Assume that the total number of array elements is N total = 100, and in this example the elements are arranged according to Figure 2 The array elements are arranged on a hemispherical surface in the manner shown. In the simulation, the polarization characteristic component of each element takes a random number between [0,1].

[0079] In order to comprehensively evaluate the performance of the present invention, this section uses Task Drop Ratio (TDR), Hit Value Ratio (HVR), Time Utilization Ratio and runtime as performance evaluation indicators. The above indicators are defined as follows:

[0080] The task loss rate (TDR) is the ratio of the number of lost tasks to the number of scheduled tasks during the simulation time:

[0081] TDR=N drop / N all (twenty three)

[0082] Among them, N drop Indicates the number of lost tasks, N all Indicates the number of tasks requested for scheduling;

[0083] Time utilization ratio (TUR): It is defined as the ratio of the total residence time of the actual execution task to the total simulation time:

[0084]

[0085] Among them, t total is the total simulation time.

[0086] The realized value rate (HVR) is the ratio of the sum of the work mode priorities of the tasks actually executed during the simulation time to the sum of the work mode priorities of the tasks applied for scheduling:

[0087]

[0088] Among them, N exe Indicates the number of tasks actually executed. This indicator is used to reflect the proportion of high-priority tasks that are successfully scheduled;

[0089] Runtime: The runtime within a scheduling interval.

[0090] The beam dwell method of the simultaneous multi-beam radar system based on polarization characteristic adaptive array element selection proposed in the present invention is adopted, and the performance is compared with method A and method B. Method A is based on the framework structure of the present method, and adopts an exhaustive method to select array element combinations for different tasks to achieve simultaneous multi-beam dwell scheduling; method B is a phased array radar beam dwell scheduling method based on time pointer (see literature: Lu Jianbin, Hu Weidong, Yu Wenxian. Research on real-time task scheduling of multifunctional phased array radar [J]. Journal of Electronics, 2006, 34 (4): 732-736.). The simulation platform is MATLAB R2019a, the computer processor is Core i7-10700, and the memory is 16G. Figures 3 to 6 The statistical results of 100 Monte Carlo tests under different indicators.

[0091] Figure 3 is the task loss rate curve. When the number of targets is 10, method B has obvious task loss, while method A and the method of the present invention only start to have slight task loss when the number of targets is 80. Both method A and the method of the present invention use the simultaneous multi-beam dwell method, so their loss rates are very similar. However, method B only executes one task at the same time, so its loss rate is much higher than that of the method of the present invention and method A.

[0092] Figure 4 is the time utilization curve. The time utilization of method B is already in a relatively saturated state, while the time utilization curves of method A and the method of the present invention increase linearly with the increase of the number of targets; when the number of targets increases to a certain extent, the increase trend of time utilization slows down. The method proposed by the present invention and method A have the greatest time utilization.

[0093] Figure 5 To achieve the value rate curve, the curve reflects whether the tasks with higher working mode priority are executed as much as possible. Since the method of the present invention and method A can execute multiple tasks at the same time, the achieved value rate is much higher than that of method B, which is opposite to the trend of their loss rate curves.

[0094] Figure 6 is the average running time of the three methods in one scheduling interval. Because method A adopts an exhaustive method, its calculation speed is the slowest. The method of the present invention adopts a heuristic method to select array elements to achieve simultaneous multi-beam resident scheduling, and the running time is greatly reduced compared with method A. Method B does not consider simultaneous multi-beams, so the analysis process is the simplest and the running speed is the fastest. It can be seen that when the number of targets reaches a certain level, the running time of method A exceeds the scheduling interval length. At this time, method A does not have real-time performance. Under different target numbers, the running time of the algorithm of the present invention is less than the scheduling interval length, and it has real-time performance.

[0095] Figure 7The figure is a comparison image of the number of array elements used by the method of the present invention and method A at different transmit powers for the same task when adaptive array element selection is performed based on polarization characteristics. The two methods differ only in the array element selection method, and the number of array elements used by them is not much different, so the performance indicators of the two methods such as loss rate, time utilization rate, and realization value rate are also very small.

[0096] In summary, compared with the scheduling method based on time pointer, the method proposed in the present invention can greatly reduce the task loss rate and improve the time utilization of the system; compared with the adaptive array element selection and simultaneous multi-beam dwell scheduling method based on the exhaustive method, this method has real-time performance and can be applied to actual radar systems. The present invention is a real-time beam dwell scheduling algorithm that realizes the simultaneous execution of multiple tasks by adaptively selecting array elements based on polarization characteristics.

Claims

1. A beam dwell scheduling method for a simultaneous multi-beam radar based on polarization characteristic adaptive array element selection, characterized by: After considering polarization, the transmission characteristics of the i-th array element can be expressed by the vector Describe (1≤i≤N total ), where θ is the pitch angle, is the azimuth, N total is the total number of array elements, is the array element i The projection of the radiation characteristics in the x direction, is the array element i The projection of the radiation characteristics in the y direction, is the array element i The projection of the radiation characteristics in the z direction; Assume that in the current scheduling interval t0,t end There are N resident tasks T = T1, T2, ..., T N Apply for scheduling, where t0 is the start time of the current scheduling interval, t end is the end time of the current scheduling interval, t end -t0 is the duration of this scheduling interval; the resident task model is Among them, rt i is the expected execution time, st i is the actual execution time, l i is the time window, p i is the working mode priority, Δt i For the length of stay, is the average power demand received by the mission, pt i is the signal transmission power, θ i , Indicates the azimuth and elevation angles of the mission; a beam dwell scheduling method for a simultaneous multi-beam radar system based on polarization characteristic adaptive array element selection comprises the following steps: Step 1: Initialize the time pointer tp, set tp = t0, i = 0; Step 2: Select the tasks in the task request queue T that satisfy rt+l<tp, and record the number of these tasks as n i , delete them from the task request queue, and then store them in the task deletion queue, i = i + n i , let M = N total ; Step 3: In the task request queue, assume that there are X tasks satisfying tp ≥ rt-l; if X>0, calculate the priority sw of each task according to formula (1) i , where Xd i Request T for the task i (1≤i≤X) is the number of tasks in descending order of deadline, Xp i It is the sequence number of X tasks arranged in ascending order of work priority; Sort these X tasks by their comprehensive priority from largest to smallest, and set itp = 1; if X = 0, update the time pointer tp = tp + Δtp min , where Δtp min is the minimum sliding step of the time pointer; after updating, if tp≥t end , then the scheduling interval analysis ends; otherwise, return to step 2; Step 4: Take the itpth task T in the sorted task queue itp ; Step 5: If tp+Δt itp >t end , then the analysis of this scheduling interval ends, Δt itp T itp Otherwise, set zy_use to empty, m=1, and execute the next step; Step 6: According to T itp The direction parameter of the task T can be found in each polarization direction of the array element by formula (2). itp The direction that best matches the target direction θ min With θ max are the minimum and maximum values ​​of the pitch angle, and are the minimum and maximum values ​​of the azimuth angle, Δθ, is the discreteness of the elevation angle and the azimuth angle; So for task T itp , M array elements in The polarization characteristics of the direction form a matrix as shown in formula (3); Step 7: Calculate the M array elements according to equation (4) The square sum of each component of the polarization characteristic of the direction is calculated and sorted from large to small, and the array element number sorted in this way is stored in zy_num; Step 8: Select the first m array elements in zy_num to calculate the power value, recorded as P cal ; Step 9: If P cal ≥P des , then M=Mm, and jump to step 11, otherwise m=m+1, and go to step 10; Step 10: If m>M, jump to step 13, otherwise, return to step 8; Step 11: T itp Put it into the task execution queue and put T itp Delete from the task request queue, set i=i+1, and store the m array element numbers used in zy_use i , represents the array element sequence number set used by task i; delete these array elements in zy, and itp The residence time is stored in t_store, itp = itp + 1; Step 12: If itp≤X and M>0, return to step 4, otherwise go to step 13; Step 13: After the scheduling analysis at time tp is completed, the time pointer tp=tpmax(t_store) is updated; Step 14: If i=N, the analysis of this scheduling interval ends, otherwise jump to step 2.

Images