With the improvement of radar digitization,digital array radar (DAR) has been widely researched in the radar industry[1]. Compared with traditional analog phased array radar, DAR not only has the advantages of high detection precision, complex target detection capability, and strong anti-jamming capability, but also has the characteristics of flexible signal processing mode. It can be used to search a number of airspaces, and track and image multiple targets simultaneously—resulting in effective time resource management of radar[2].

Reasonable, flexible and effective scheduling strategies are the key to exploiting the high adaptive potential of DAR. Among existing studies, there are mainly two ways to implement resource management of DAR: template-based scheduling and adaptive scheduling. Adaptive scheduling methods flexibly adjust the resource scheduling strategy according to the working environment and task requirements, and are the most effective but also the most complex scheduling methods[3].

So far, many scholars have studied the radar resource scheduling model. In Ref.[4], an adaptive algorithm of phased array radar based on time window is proposed to verify the rationality and validity of introducing time window in the scheduling process. A resource allocation model based on “Quality of Service” is proposed in Ref.[5] to optimize the target tracking performance of phased array radar systems. In Ref.[6], an adaptive scheduling algorithm based on information entropy is proposed to solve the optimal searching problem in target regions. In order to further improve the source utilization ratio of the radar system and give full play to the advantages of multifunction digital array radar, pulse interleaving technology is proposed. Its core idea is to schedule the transmission or reception pulse of other tasks in a single task pulse interval. Orman analyzed this method in Ref.[7] and proposed a heuristic algorithm to solve the problem of adaptive beam-dwell scheduling for phased array radar. In Ref.[8], an optimal algorithm based on pulse interleaving for radar task quadratic programming model is proposed to improve the scheduling success ratio of tasks with high priority. Aiming at the problem of beam-dwell scheduling for DAR, an algorithm based on analyzing scheduling interval is proposed in Ref.[9]. However, in almost all existing adaptive resource scheduling methods for DAR, the imaging mission is not taken into account. Joint scheduling imaging tasks with search, tracking and other tasks not only improve the recognition ability of the radar to the target and give full play to the advantages of multi-task cooperation, but also feedback the target characteristic information obtained by the image to the transmitter radar system.This enables the realization of dynamic adjustment of imaging tasks and improves the resource utilization ratio[10]. Traditional imaging algorithms require continuous observation of targets for a long time to obtain high-resolution images, but the alternation of different tasks inevitably leads to discontinuous synthetic aperture sampling of the imaging target azimuth.

Based on the above issues, in this paper we propose a dwell scheduling algorithm for DAR, which takes the imaging task requirements into account in the radar resource scheduling model, by using the compressed sensing (CS) ISAR imaging method.

1 Task Model and Constraints Based on Pulse Interleaving

DAR is a kind of all-digital phased array radar, which can receive and transmit the beam in a digital way. It can be interleaved in the form as shown in Fig.1. txj,twj,trj denote the radar beam transmitting duration, waiting duration of a dwell, and the radar beam receiving duration respectively for j(j=1,2).With the pulse interleaving technology in DAR, time resources of the waiting duration can transmit or receive other resident tasks,and furthermore, the receiving duration of dwell tasks can overlap each other at the same time.

因为存在k不等于整数的情况，所以随机抽样时先对k取整.根据首次入侵发起时间点t1(0≤t1

Fig.1 Form of pulse interleaving in DAR

1.1 Sparse aperture imaging based on compressed sensing

In order to measure the performance of the radar resource scheduling, the scheduling success ratio (SSR), the hit value ratio (HVR), the time utilization ratio (TUR) and the energy utilization radio (EUR) are taken as the criterion. They can be expressed as

蛋白质是构成一切细胞和组织结构必不可少的成分，它是动物生命活动最重要的物质基础。适宜的蛋白水平对满足蛋鸡生产需要和饲料资源的合理应用具有重要意义。通过饲养试验研究“京红1号”蛋种鸡育成期的蛋白质需要量，旨在为制定“京红1号”蛋种鸡饲养标准提供依据。

In order to improve the adaptive ability of radar imaging, the method proposed in Ref.[10] can be used to recognize the characteristics of the targets after entering the stable tracking phase, and then calculate the demand of radar resources for target imaging based on the cognitive results. We estimate the distance i, speed i, heading i, target size i, sparsity of echo in Doppler domain i and observation time ci of the i-th target. Assuming that the target is non-maneuvering, the full aperture imaging of the radar needs to transmit Ni=Pfci pulses (Pf is the pulse repetition frequency), and the measurement dimension Mi(Mi<Ni) after dimension reduction is then expressed as

In order to make better use of the time resources of DAR to image as many precise tracking targets as possible, we propose the self-adaptive adjustment strategy of the imaging accumulation time of different imaging targets. After the end of each scheduling interval, the ISAR image of the target is reconstructed by using all of the previous observed sub-pulses up to the scheduling interval.

Mi≥cilnNi

(1)

where c is a constant associated with the recovery accuracy, usually taken as 0.5-2(we assume c=1 in this paper).

1.2 Radar dwell model

The DAR dwell model is defined as

T={et,st,tx,tw,tr,ω,M,pri,Pt,P}

(2)

where et denotes the expected scheduling time; st denotes the actual scheduling time; tx,tw,tr denote the transmitting duration, waiting duration and receiving duration respectively; ω denotes the time window of the task; M denotes the number of pulse repetitions in the search and tracking tasks, and denotes the azimuth-oriented observation dimension in the imaging task; pri denotes the pulse repetition reputation interval; Pt denotes the pulse transmitting power; and P denotes the task priority[13].

1.3 Scheduling constraints

For tracking and imaging tasks, assuming the distance from the ith target to the radar is i, the waiting duration for the ith task dwell can be calculated from the predicted position information of the target, which is given by

twi=2i/c

(3)

For the search tasks, it is generally impossible to obtain the arrival time of the echo in the absence of prior information. Therefore, in order to ensure that radar echo signals can be effectively received after the searching pulse is transmitted, once the transmitting duration ends, the antenna system must be in the receiving state until the maximum waiting time, i.e. the waiting duration of the search task dwell cannot be preempted.

It should be noted that the arrival time of radar echo is affected by the range size of the target.In order to ensure the imaging quality, the received pulse should be broadened properly. Suppose that the distance from the i-t target to the radar is i and the range size of the target is yi, the width of the actual received pulse of the ith imaging task can be expressed as

twi=2(i+yi)/c

(4)

Although the overlap of multiple dwell tasks can improve the resource utilization of DAR, the energy consumption of the system is bound to increase as the radar is in the transmitting state for a long time. In order to avoid the damage of the transmitter due to the long working time, the restriction of energy constraint must be considered in the scheduling algorithm. The transient energy of the system at t moment can be expressed as

E(t)=P(x)e(x-t)/τdx

(5)

where P(x) is the power parameter, and τ is the look-back period, which is related to the heat transfer of the system. The energy constraint of the system can be defined as that E(t) cannot exceed the maximum threshold Emax of instantaneous energy at any time, i.e.

E(t)≤Emax

(6)

In terms of the above performance index, assume that there are N dwell tasks in the scheduling interval [t0,te], an effective model of DAR based on pulse interleaving can be defined as

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In simulation, the energy consumption of radar beam and the variation of energy state in time Δt can be estimated in prior by the parameters of antenna gain, transmission power, pulse width and pulse number, so as to reduce the complexity of algorithm.

2 Dwell Scheduling Algorithm for DAR

2.1 Design of task priority

Without loss of generality, the target at a closer distance, higher speed and moving toward the radar is more threatening and requires a higher priority for tracking and imaging. If the tracking is divided into precision tracking and normal tracking, the ith priority of the precision tracking task and the normal tracking task is defined as

(7)

(8)

where and a1,a2,a3(a1,a2,a3≥0,a1+a2+a3=1) are adjustment factors representing the impact degree of different target information on priority. Obviously, the priority design method will control the priority range for the precision tracking task in 2-3, and the priority range for the normal tracking task in 1-2.

We divided the search task into high priority search (with priority of 3) and low priority search (with priority of 1). We assume only one verification beam is transmitted for confirmation after searching for a new target. Then the new target is added to the existing tracking task list to recognize the feature, calculate the tracking priority, and scheduled within the next scheduling interval.

When a precise tracking task enters the stable tracking phase (assume radar enters the stable tracking phase after transmitting li beam to track), the strategy of tracking and imaging are adopted at the same time in the next scheduling interval. The priority of the ith imaging task that enters the stable tracking phase is defined as

(9)

Obviously, the priority of the imaging task is between 0 and 1, which is ensured to be lower than the priority of search and tracking tasks. The scheduling of an imaging task usually takes several scheduling intervals, in order to ensure that the pulses transmitted by the radar are not wasted during the imaging process, and a priority dynamic adjustment strategy is adopted for imaging tasks. If ith imaging task is implemented in the kth scheduling interval, the priority of the ith imaging task should be increased appropriately when allocating resources to the next scheduling interval.

Pi,k+1=Pi,k+ΔP

(10)

where ΔP is the step value of priority.

2.2 Adaptive adjustment of imaging accumulation time

前言:肿瘤组织间碘-125放射性粒子植入术作为近年来治疗恶性肿瘤的方式,效果良好[1]。手术可在CT指导下将放射性离子植入肿瘤内部,使肿瘤组织遭到毁灭性杀伤,从而达到治疗的目的[2]。但是手术过后需要对患者开展细致的护理工作,才能够保证手术效果,为患者延续生命。常规护理模式效果并不理想,有待完善。故本文选取49例肿瘤患者,对其开展肿瘤组织间碘-125放射性粒子植入术,后采用围手术期护理,取得了良好的效果,现报道如下。

Generally, as the imaging accumulation time increases, the quality of ISAR images increase accordingly and gradually come to a standstill. After reaching the standstill, the quality of ISAR image become worse if the imaging accumulation time continues to increase. Therefore, the mutual information can be taken as the similarity measure of adjacent reconstructed ISAR image. Mutual information represents the amount of information that two images contain about each other. For adjacent reconstructed images A and B, their mutual information I(A,B) is expressed as

(11)

where pi,pj denote the gray probability distribution of A and B respectively, and pij denotes the joint gray probability distribution. The larger the value I(A,B) is, the higher the similarity of the two structure image is. After selecting an appropriate threshold Tα by reference to the desired resolution, if the mutual information of the target ISAR image obtained after the two adjacent scheduling intervals is less than the threshold Tα, continue to analyze the imaging task in the next scheduling interval.If the mutual information is more than the threshold Tα, it is considered that the imaging quality of target is up to the expected standard, and the imaging task is finished.

2.3 Dwell scheduling algorithm

The traditional DAR needs to separate part of the continuous time resources to achieve imaging capabilities in the implementation of the target searching and tracking, which leads to the contradiction of the radar resource allocation and low radar efficiency. Under the framework of CS theory, continuous observation of the target image can be transformed into random sparse observation, and high-quality target ISAR image can be obtained under sparse aperture condition. This provides an effective technical support for incorporating imaging task requirements into the DAR resource scheduling model.

在我国当前农机推广服务工作中由于人员自身素质原因仍秉承着传统的服务模式，无法适应现阶段高节奏的社会发展速度，因此需要对服务模式进行创新和变革。具体可以在推广工作中，积极引入现代信息技术，最大限度的提升基层农机推广效果，建立完善的基层农机推广服务体系。以此同时，要由政府对推广服务体系进行统一管理，并聘请专业人员进行现场指导，让农民直接参与其中，提升其对农机的接受度，促进农机推广可持续发展。

SSR=N′/N

(12)

(13)

(14)

(15)

where N is the total number of tasks for requested scheduling, N′ is the number of scheduled tasks, Tt is total simulation time, Pt is the peak power of each transmitted pulse and Pav is the average power delivered by the radar.

which means E(t) cannot exceed the maximum threshold Emax of instantaneous energy at any time.

(16)

If the task meets the time and energy constraints in Eq.(16), it will be sent to the execution list and removed from the application list. The time slot vector U and time pointer tp can be rewritten as follows.

The nonlinear programming problem in Eq.(16) is an N-P problem, and it is difficult to obtain the optimal solution. As a consequence, heuristic algorithms are usually used to obtain sub-optimal solutions[16]. With the self-adaptive adjustment strategy based on pulse interleaving, a heuristic method for solving the optimization problem is given. The effective algorithm of DAR based on pulse interleaving is summarized as follows.

D= te-t0Δt ,

Step 1 Take N tasks for requested scheduling in the scheduling interval [t0,te], add K tasks with the latest scheduled start time less than t0 to the delete list, discretize the system time; suppose that the length of each time slot is Δt, the number of time slot is introduce time pointer tp=t0, initialize the time slot vector U={u1,u2,…uD}=0 and energy state vector E.

Step 2 Let the remaining N-K tasks join the application list according to the corresponding priority from high to low (tasks with the same priority are arranged according to the expected execution time), and let i=1.

由于可溶性Cl具有不完全燃烧及键能较高的特点，部分NaCl燃烧后仍残留在底灰中，基于上述的分析结果可知，利用传统的热处理（燃烧）方法较难准确测量厨余垃圾中Cl含量。因此，对于城市固体废弃物中的可溶性 Cl含量宜采用水萃取法来测定，水萃取法可对固体废弃物中的可溶性Cl和不溶性Cl进行区分，并能准确标定可溶性Cl的含量，这对预测Cl的热动性及Cl元素在热转化过程中引起的腐蚀问题的研究具有重要意义。

Step 3 Determine whether the ith task can be scheduled at time tp.

where N′ is the number of search tasks and q1,q2,q3,q4 are adjustment factors. The first constraint gives the scope of the actual execution time of each task; the second constraint indicates that there is no conflict between the transmitted pulses, i.e. the transmitting duration of the radar task cannot be preempted; the third constraint indicates that the search tasks cannot perform pulse interleaving; the fourth constraint indicates that the task dwell received pulse can be overlapped in the same time without colliding with the transmitted pulse; and the fifth constraint represents the energy constraint for task scheduling.

Step 5 If i≤N-K, return to step 3, otherwise go to step 6.

uk=1,k∈( stiΔt , sti+txi+twi+triΔt )

(17)

tp=sti+txi+twi+tri

(18)

Case 2: Tracking tasks

另一种金属盐——硫酸铜也可作安全的蚀刻剂使用，主要用于腐蚀锌版和铝版。其腐蚀原理与氯化铁类似，如以锌版蚀刻为例：

uk=2,k∈

( sti+npriiΔt , sti+txi+twi+tri+npriiΔt )

(19)

tp=sti+txi

(20)

Case 3: Imaging tasks

uk=3,k∈( stΔt , sti+txi+twi+triΔt )

(21)

tp=sti+txi

(22)

In order to distinguish different task types, the time slots uk are assigned 1, 2 and 3 respectively. Update the energy state vector E=E+ΔE(ΔE is the system energy consumption change), let i=i+1, and return to step 3. If the scheduling fails, adjust the actual execution time of the task in the time window, and let tp=tp+Δtp(Δtp is the minimum step size of the pointer slide).

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Step 4 If tp<st+ωi, return to step 3, otherwise the task cannot be scheduled. Add it to the delete list, let i=i+1.

Case 1: Search tasks

扬中市智慧城市建设离不开创新驱动，创新驱动离不开“城市智库”——具备信息技术、互联网知识的创新型人才，因此必须解决好高端专业人才匮乏的问题。科研单位需要与高校相结合，从产业升级的需要出发，培养实用性强、操作性强的复合型人才，为优化扬中市智慧城市建设出谋划策。此外，要建立健全创新型人才引进、储备、使用和成长的良性机制，从满足人才自身需要出发，激发人才创新潜能，调动人才参与扬中智慧城市建设的积极性，为优化扬中智慧城市建设方案贡献力量。

Step 6 The scheduling analysis of the scheduling interval ends. Use the sparse-aperture ISAR imaging method for target imaging by using all of the previously observed sub-pulses up to this scheduling interval. When the mutual information is more than the predefined threshold, this imaging task is no longer scheduled in the next scheduling interval. Otherwise, put the imaging task into the next scheduling interval for analysis.

(2)在PPT设计时要全面考虑PPT要素的取舍，让学生既能聚焦重难点内容，又不要感到过于单调、乏味，保证自主学习重难点内容的学习效果。

The flow chart of the scheduling process in one scheduling interval is as shown in Fig.2.

Fig.2 Flow chart of the scheduling process

3 Simulation and Analysis

In the simulation, we choose three kinds of radar working mode: search, tracking and imaging. Typical parameters for various tasks are summarized in Tab. 1. The total simulation time was 6 s, the scheduling interval length was 50 ms, and the radar can provide an average power of 400 W. For search and tracking tasks, radar transmits narrowband signals, center frequency fc=10 GHz, signal bandwidth B=10 MHz, and pulse repetition frequency Pf=1 000 Hz. For imaging tasks, radar transmits LFM signals, center frequency fc=10 GHz, signal bandwidth B=300 MHz, pulse repetition frequency Pf=1 000 Hz, and priority sliding step ΔP=0.1.

Tab.1 Parameters of radar tasks

TasktypePriorityDwelltime/msTimewindow/msUpdaterate/HzPulseduration/msTransmittingpower/kWHigh-prioritysearching3310200.023Precisiontracking2-3220100.014Normaltracking1-223050.014ISARimaging0-1120-0.015Low-prioritysearching0310100.023

Traditional phased array radar algorithm (traditional algorithm)[15], the pulse interleaving scheduling algorithm(simple task algorithm) which does not consider the imaging tasks[9] and the adaptive dwell scheduling algorithm proposed in this paper (proposed algorithm) are compared in the simulation. Comparison curves of three different algorithms are shown in Tab.2-Tab.5.

指标体系是国土空间规划编制的基础依据，因此要不断完善指标体系。需要注意的是，国土空间规划编制的指标体系必须结合区域的实际情况，坚持一切从实际出发原则，进而提高国土空间规划编制的水平。此外，在新形势下国土空间规划编制的指标体系还应该综合考虑各项因素，综合做好生态文明建设、乡村振兴、精准扶贫、区域协调、可持续发展等指标设置。例如：坚持绿色发展，落实生态文明建设要求，强化生态保护红线、山水林田湖草系统治理、新增水土流失治理面积等指标；实施乡村振兴战略，统筹安排人均农民收入增量、投资规模增量、基础设施增量、农村产业增加值、农村人居环境整治等指标。

Tab.2 Scheduling success ratio %

Tasknumber20406080100Proposedalgorithm1001001009581Traditionalalgorithm10084654520Simplealgorithm100100957357

Tab.3 Hit value ratio %

Tasknumber20406080100Proposedalgorithm10010010010083Traditionalalgorithm10061343021Simplealgorithm1001001007866

Tab.4 Time utilization ratio %

Tasknumber20406080100Proposedalgorithm3262727577Traditionalalgorithm910101010Simplealgorithm2949565656

Tab.5 Energy utilization ratio %

Tasknumber20406080100Proposedalgorithm3047566859Traditionalalgorithm810101010Simplealgorithm2540494949

From Tab.2, we see that when the number of tasks is 20, system resources are relatively abundant and the competition for resources among tasks is not obvious. All the three scheduling algorithms can successfully schedule all tasks. With the further increase of the tasks, the scheduling success radio of the traditional algorithm begins to decline significantly, while the other two algorithms based on the pulse interleaving can still successfully schedule all tasks. When the number of tasks increased to 60, the simple task algorithm cannot schedule more tasks, but the proposed algorithm can successfully schedule all tasks.This is due to the saturation of radar resources in the simple task algorithm.In the proposed algorithm, the imaging tasks have the lowest priority, so the remaining resources of the system can be fully utilized by the dynamic adjustment of the imaging accumulation time and the flexible sparse aperture allocation, without affecting the scheduling of the search and tracking tasks. Consequently, the task number of successful scheduling is improved.

From Tab.3, we see that when the number of tasks is 20, the system resources are relatively abundant; but when the number of tasks increased to 40, the hit value ratio of traditional algorithm has fallen to a great extent. The precision tracking task can be imaged with the idle time of searching and tracking in proposed algorithm, so that it maintains a high hit value radio when the number of tasks reaches 80.

From Tab.4 and Tab.5, we see that when the number of tasks is 20, the time utilization ratio and the energy utilization ratio plateau at 0.1 because of the resource bottleneck in traditional algorithm. Through the use of the pulse interleaving technology, the simple task algorithm can further utilize the radar system resources, the time utilization ratio can reach about 0.57 and energy utilization can reach about 0.5. On the basis of pulse interleaving, the idle time of search and tracking task is fully exploited in the proposed algorithm, so the time utilization ratio and energy utilization ratio can reach about 0.75 and 0.6 respectively.

In order to validate that the DAR can achieve the target imaging while searching and tracking, the imaging results of three imaging tasks above are compared with the traditional full aperture ISAR imaging results, and the peak signal to noise ratio (PSNR) is used to measure the effect of the proposed algorithm. The PSNR is defined as

本文中相关电能替代领域选择的体系应该包含所有可能存在的电能替代领域，然后综合考虑，建立健全的指标体系[14-16]，进行形成科学、合理的评估体系。本文中的指标体系如图1所示。

(23)

where σ(i,j) denotes the sparse aperture imaging result in this paper, σ(i,j) denotes the traditional full aperture imaging result, m and n denote the number of rows and columns of the ISAR image matrix respectively. The larger the PSNR value, the better the imaging effect. The contrast between the traditional full aperture imaging and the sparse aperture imaging in this paper is shown in Tab.6. From Tab.6, it is shown that the proposed imaging method can be used to solve the problem of azimuth aperture sparsity and obtain satisfactory image quality.

Tab.6 Comparison of the image quality by the conventional full aperture and the sparse aperture

4 Conclusion

In this paper, a dwell scheduling algorithm has been proposed based on pulse interleaving for DAR. The time and energy constraints are set respectively, and the optimal resource scheduling algorithm is established. The simulation results show that the proposed algorithm can accomplish tracking and search task effectively as well as obtain high quality sparse aperture ISAR image. It not only makes use of the multi-task cooperative advantage of DAR, but also improves the resource utilization ratio of radar system. It should be noted that, in this paper, we assume that the target is non-maneuvering and the maneuverability of the target in the actual imaging process is ignored. For the target imaging of maneuvering flight, in addition to the sparsity of the azimuthal aperture, the optimal imaging time and the quality evaluation criteria of the imaging should be considered. Related content should be further studied.

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此外，随着人本主义、后现代主义浪潮的兴起，学者开始从社会文化地理视角对旅游者的地方感（万基财、张捷、卢韶婧等，2014）、地方依恋（苏勤、钱树伟，2012）、地方认同等进行理论化探讨，初步厘清了旅游者与地方的深层次联系。通过不同研究视角的多方位解读，国内旅游者行为研究正在朝着科学化、多元化的方向迈进。