Aiming at optimizing the allocation problem of limited resources in a radar network, a resource scheduling algorithm combining pulse interleaving with preallocation is proposed for multitarget inverse synthetic aperture radar imaging. The imaging method adopts compressed sensing, which only needs to emit a small number of pulses so that we can set the algorithms to schedule the allocation of the pulses over a period of time. The authors point out the problem of pulse conflict, which is ignored in the process of the scheduling algorithm and proposes a preallocation method to avoid the occurrence of the conflict. Meanwhile, pulse interleaving is added to increase the positions of the dispatchable pulses. Moreover, the combined algorithm can perform adaptive scheduling on the radar time resource according to the feature parameters after target feature cognitive. Finally, the feasibility of the combined algorithm is verified by the simulation, and two performance indicators, the hit value rate and the pulse utilization rate, are improved by the proposed algorithm. |
1.IntroductionWith the complexity and diversity of radar application scenes and the increase in noncooperative targets in the air, it is difficult to obtain more comprehensive target information only relying on a single radar to image the target. Therefore, the application and rise of radar networks are imperative, and it also requires more tasks to be performed with limited radar resources.1–3 Adaptive scheduling is the most effective method among many resource scheduling methods. By introducing the idea of cognition and further improving the adaptive ability of radar network resource scheduling, the success rate of task scheduling can be greatly improved.4,5 Besides, compressed sensing (CS) plays a very important role in sparse inverse synthetic aperture radar (ISAR) imaging and saves considerable resources for other tasks.6–8 To date, some scholars have performed much research on resource scheduling. For example, a joint antenna layout and transmission power distribution algorithm was proposed to improve the monitoring performance of a distributed radar network in Ref. 9. Yan et al.10 proposed an optimal antenna deployment algorithm for the problem of multiregion simultaneous interference. Furthermore, Tian et al.11 proposed a time-constrained task scheduling algorithm for a multifunctional radar network task scheduling problem and verified the effectiveness of the algorithm. These studies all focus on resource scheduling for target detection, tracking, location, and target feature cognition. At present, there are relatively few studies on the scheduling of imaging resources in radar networks. However, imaging needs to occupy most of the resources, so the reasonable allocation of imaging resources can save more resources for the radar to perform more tasks.12–14 The model established in Ref. 15 optimizes resource allocation for multiobjective imaging tasks in radar networks, but it uses the traditional Rang–Doppler (RD) imaging algorithm, which, although effective for traditional algorithm, is not as superior as CS. An allocation method of resource scheduling based on sparse observation ISAR imaging was proposed in Ref. 16, but it uses the allocation method based on pulse dwell time. On the other hand, Chen et al. introduced pulse interleaving technique to break through the original resource saturation upper limit that makes full use of the waiting time between transmitting and receiving pulses and maximizes the use of radar resources.17 However, both studies were carried out on a single radar. A radar network is different from a single radar in that it is necessary to consider the conflict that arises from the same frequency pulse of multiple radars for a certain target. Based on the recognition of target characteristics, the proposed algorithm calculates the pulse number needed for the sparse observation of each target. Then, preallocation and pulse interleaving are used for adaptive allocation. Finally, the resource scheduling for multiple targets in the timing sequence of multiple radars is completed. The rest of this paper is organized as follows. Section 2 introduces the concept of cognition and how to obtain cognitive parameters. Section 3 introduces the core technical support for this scheduling algorithm: preallocation and pulse interleaving. Furthermore, the imaging model of the radar network resource scheduling algorithm is established. Section 4 gives the experimental simulation results and analysis. Finally, Sec. 5 draws the conclusions. 2.Cognition of Target CharacteristicsThrough learning from the surrounding environment, combining with prior information and reasoning, cognitive radar constantly adjusts the transmitter to realize feedback between receiver and transmitter so as to improve the overall performance of radars. After receiving the echo signal, the cognitive radar network can calculate the specific information of the detected target using the conventional tracking algorithm of the traditional radar: the range , the velocity , and the angle that between the target and the center of the radar beam of the ’th radar to the ’th target. The other parameters according to Ref. 16 are calculated as follows:
3.Scheduling Algorithm3.1.PreallocationWhen sparse ISAR uses CS to reconstruct image information, it is easy to see the phenomenon shown in Fig. 1, where multiple radars image a target. It shows that the simultaneous pulse transmission of multiple radars to the target at some time causes mutual interference among the radars and affects the echo signal. To be more specific, each radar is only eager to receive its own signals. When multiple radars transmit the same frequency signal at the same time, the receiver cannot judge which signal is transmitted by the same radar transmitter, thus causing interference. Consequently, if this situation is not avoided, it will not only waste the resources but also will affect the imaging effect when the radar resources are not adequately allocated. Therefore, the transit scheduling interval can be used to preallocate each target, to avoid this kind of conflict. The specific method is shown in Fig. 2, where represents the virtual scheduling interval of the ’th target. Considering three radars imaging the same target, the detailed steps of preallocation are described below.
Because of the sparsity, it is possible to allocate several radars in one transit scheduling interval without conflict. However, if only the pulse conflict is reduced, the conflict is not serious when the number of targets is small. And less spare time can be allocated when the number of targets is large, but it can prevent low-priority tasks from overwriting high-priority tasks because they are allocated in order of priority. Hence in both cases, the improvements of resource utilization rate and scheduling success rate (SSR) are not very great in the radar network. Furthermore, this theory is verified by simulation in Sec. 4 of this paper. Therefore, pulse interleaving is proposed to provide more resources to be allocated when there are more targets. Although Ref. 17 completed the application of pulse interleaving for a single radar, research on networking has not been further studied. 3.2.Pulse InterleavingThe dwell time of the radar task includes three processes: pulse transmitting, waiting, and receiving. Most studies regard the three parts as a whole, which wastes the intermediate waiting time. Pulse interleaving is used to insert other tasks into the waiting time to make full use of the resources, and it can be expressed in Fig. 3. The two interleaving cases of pulse interleaving were introduced, corresponding to the left and right cases in Fig. 3, respectively. And the time constraints of the two cases are as follows: where is the length of time to transmit the pulse, is waiting time for between the transmitting and receiving pulses, and is the length of time to receive the pulse. As long as there is no conflict between the pulses no matter what the case is adopted, and the spare time is fully used, the utilization rate of pulse resources can be improved.3.3.Algorithm ModeSince there are many variable factors, we can define several positive indexes of the scheduling algorithm and construct the objective function from these performance indicators so that we can obtain the optimal solution by finding the maximum value of the objective function under some constraints in the algorithm model. Therefore, two resource scheduling performance indicators can be defined.
The above are the constraints of the combined algorithm in the radar network that we proposed. After applying these constraints, the random time sequence results of each subradar of the radar network with multiple targets can be obtained. Although a genetic algorithm can be used to obtain the optimal solution,20 considering the randomness of CS, the solution was obtained directly under the constraint condition of completion. In addition, the idea of greedy algorithm21 is used to allocate as many resources as possible when using preallocation. Therefore, the final solution steps are as follows:
The algorithm process of radar resource scheduling based on pulse interleaving is shown in Fig. 4. 4.Simulation ResultsSimulation experiments are performed to verify the validity and superiority of the proposed task allocation and scheduling algorithm for a radar network. It is assumed that the system of the radar network is composed of six noncollinear ISARs on the ground, which are denoted by . There are eight targets that need to be imaged in the air, which are represented by . Assume that all radars emit chirp signals, the carrier bandwidth , the carrier frequency , the pulse width , and the pulse repetition frequency . To ensure a sufficient scheduling interval in the case of multiple targets, it is assumed that the number of reconstructed observation dimension for each radar is 10,000 (1 s of observation time). First, the set scene is used to obtain the coarse resolution image of the target according to the traditional ISAR imaging method. Then, the values of various characteristics of the target are calculated by the equations in Sec. 2. The parameters of the observation dimension, coherent accumulation time, and distance are shown in Tables 1Table 2–3, respectively (all three tables are the result of the product with the radar selection matrix). Table 1The coherent accumulation time of each target in each radar (0.1 ms).
Table 2The observation dimensions of each target corresponding to each radar.
Table 3Distance between each target and each radar (km).
According to the distances in Table 3, the dwell time is times that of a single transceiver pulse. If the dwell time of each pulse is taken as the minimum unit, the number of points in Table 1 will be of the original data, and the number of observation dimension in per radar is 1000. At this time, the number of observation dimension required by each radar in Table 2 is more than 2000, and the imaging of each target cannot be completed. Therefore, the use of pulse interleaving can break through the upper limit of the original resource saturation and improve the resource utilization rate. Following the algorithm process introduced in Sec. 3, the pulse time sequence diagram of each radar can be obtained as shown in Fig. 5(a), which shows the distribution of the first 100 points intercepted. In this figure, arrows are marked under the time sequence diagram of radar 6. The whole length of one arrow represents the dwell time, and the two ends are transmitting and receiving pulses. In general, it can be seen that more signals can be transmitted within the same period of time after using combined algorithm to make full use of resources. For the convenience of observation in the above experimental simulation, the observation times of multiple targets are relatively concentrated, i.e., the observation start time is relatively close, which should be relatively dispersed in the actual situation so that the timing sequence of each radar is continuous. The allocation of observation time of multiple targets in the radar network can be referred to Refs. 15 and 22. The two performance indicators, HVR and PUR, will be used to compare the differences of the proposed algorithm and the traditional algorithm. According to the calculation method of the two indicators, the results of the four algorithms under different target numbers are shown in Figs. 6 and 7, where the ratio is the average value after 50 Monte Carlo experiments. In Figs. 6 and 7, the traditional algorithm is the algorithm that does not use the pulse interleaving technique and preallocation technique such as Ref. 18. It is only used to image sparse targets with CS without other improvements, which is easy to cause pulse conflicts and high-priority be covered. The preallocation algorithm is the algorithm that adds the preallocation technique to the traditional algorithm. Likewise, the interleaving algorithm is the algorithm that adds the interleaving technique to the traditional algorithm. And the combined algorithm is the algorithm that uses the preallocation and pulse interleaving technique. In terms of preallocation, compared with the traditional algorithm and preallocation algorithm, preallocation algorithm has less improvement on the basis of traditional algorithm. But compared with the combined algorithm and the interleaving algorithm, the effect of preallocation is amplified and combined with the interleaving algorithm well. In other words, the combination of preallocation technique and interleaving technique can enlarge the effect of each other. For pulse interleaving, its improvement is obvious because both the pulse interleaving algorithm and the combined algorithm using pulse interleaving technique are much higher value of PUR and HVR than the traditional algorithm and the pre-allocation algorithm without pulse interleaving. In the end, the combined algorithm is the best one whether it is in Fig. 6 or Fig. 7. Compared with the traditional algorithm, the interleaving algorithm makes full use of the waiting time for pulse interleaving, whereas the traditional algorithm only occupies the transmitting and receiving pulse position of dwell time. Therefore, under the same resource, the utilization rate of the pulse resource is approximately times that of the traditional algorithm. This paper set up a dwell time used in the traditional unit that is 10 times that of a single pulse, so when finishing all the allocation of resources, the utilization rate of the pulse in the process of the interleaving algorithm can achieve five times that of the traditional algorithm. However, the waiting time of a target in a radar is fixed, and it needs to meet the requirements of transmitting and receiving pulses in a radar timing sequence simultaneously. Hence some separate spare positions cannot be used, and the final rate will be less than five times that of the traditional algorithm. It is times that of the traditional algorithm, which is in line with the result shown in Fig. 7. Due to the random distribution of CS, the ratios of different target numbers in Figs. 6 and 7 vary slightly and are related to the set observation dimension, coherent accumulation time, radar observation number, and other parameters. Although there may be slight fluctuations at each point, the trends shown in the figures are consistent with the theoretical analysis of this component. To visually observe the difference of the final imaging results, the scattered points of a target in the air are assumed as shown in Fig. 8, and the above four algorithms are used to image the air target as shown in Fig. 9. It can be seen from Fig. 7 that the PUR of each algorithm is different, so within the same time length, the number of effective pulses that each algorithm can transmit is different. According to the data in Table 1–3, the simulation experiment found that the conflict points in the timing sequence were about 30% of the total resource points, and the echo signals of these conflict pulses could not be used as effective information. Therefore, if we assume that the combined algorithm can transmit 500 effective pulses over a period of time. If no preallocation technique is used, the interleaving algorithm can transmit 350 effective pulses. It can be seen from the above conclusion that the combined algorithm’s pulse resource utilization ratio is about 4.5 times that of the traditional algorithm. Hence, the traditional algorithm can transmit 111 effective pulses, whereas the number of pulses that the preallocation algorithm can transmit is slightly larger than that of the traditional algorithm, which is set as 120. Through these data and CS techniques, simulation results of the four algorithms in Fig. 9 are obtained. It can be seen that within certain resources, with the improvement of the utilization rate of pulse resources, the imaging effect is better. At the same time, it also reflects the great improvement of ISAR imaging in the combined algorithm proposed in this paper. 5.ConclusionIn this paper, we first studied the sparse ISAR imaging based on cognition and found that the problem of pulse conflict has been ignored when using CS imaging. Aiming at solving the problem, we proposed a method of preallocation that can be well combined with the pulse interleaving algorithm. The simulation results show that the combined algorithm can improve the pulse utilization ratio and hit value ratio so that the radar can perform more tasks. At the same time, the clearer image with the combined algorithm proves that it can complete the task with fewer resources. Moreover, we think it can be used not only for imaging of radar network but also for tracking and searching, and even for various multidimensional random scheduling problems. It should be noted that in this paper, we assume that the transmit pulse without energy constraint. But we take into account the time of receiving the pulse, which did not need too much energy. In our future work, we will continue to optimize the algorithm with more actual constraints and try to experiment in the actual scenario. AcknowledgmentsThis work was supported by the National Natural Science Foundation of China (Grant Nos. 61631019, 61701128), Guangxi Science and Technology Department Project (AD18281061), and Postgraduate Innovation Program Project (2021YCXS038). ReferencesT. A. Severson and D. A. Paley,
“Distributed multitarget search and track assignment with consensus-based coordination,”
IEEE Sens. J., 15
(2), 864
–875
(2015). https://doi.org/10.1109/JSEN.2014.2355200 ISJEAZ 1530-437X Google Scholar
Q. Liu et al.,
“Radar assignment for stealth targets detection and tracking based on BPSO in air-defense radar network,”
in IET Int. Radar Conf.,
1
–5
(2013). https://doi.org/10.1049/cp.2013.0307 Google Scholar
H. Griffiths,
“Developments in bistatic and networked radar,”
in Proc. IEEE CIE Int. Conf. Radar,
10
–13
(2011). https://doi.org/10.1109/CIE-Radar.2011.6159708 Google Scholar
K. L. Bell et al.,
“Cognitive radar framework for target detection and tracking,”
IEEE J. Sel. Top. Signal Process., 9
(8), 1427
–1439
(2015). https://doi.org/10.1109/JSTSP.2015.2465304 Google Scholar
J. Yan et al.,
“Joint threshold adjustment and power allocation for cognitive target tracking in asynchronous radar network,”
IEEE Trans. Signal Process., 65
(12), 3094
–3106
(2017). https://doi.org/10.1109/TSP.2017.2679693 ITPRED 1053-587X Google Scholar
S. Zhang, Y. Liu and X. Li,
“Autofocusing for sparse aperture ISAR imaging based on joint constraint of sparsity and minimum entropy,”
IEEE J. Sel. Top. Appl. Earth Obs. Remote Sens., 10
(3), 998
–1011
(2017). https://doi.org/10.1109/JSTARS.2016.2598880 Google Scholar
S. Zhang et al.,
“High-resolution bistatic ISAR imaging based on two-dimensional compressed sensing,”
IEEE Trans. Antennas Propag., 63
(5), 2098
–2111
(2015). https://doi.org/10.1109/TAP.2015.2408337 IETPAK 0018-926X Google Scholar
P. Cheng et al.,
“A fast and accurate compressed sensing reconstruction algorithm for ISAR imaging,”
IEEE Access, 7 157019
–157026
(2019). https://doi.org/10.1109/ACCESS.2019.2949756 Google Scholar
Y. Yang et al.,
“Multi-static radar power allocation for multi-stage stochastic task of missile interception,”
IET Radar Sonar Navig., 12
(5), 540
–548
(2018). https://doi.org/10.1049/iet-rsn.2017.0534 Google Scholar
J. Yan et al.,
“Power allocation algorithm for target tracking in unmodulated continuous wave radar network,”
IEEE Sens. J., 15
(2), 1098
–1108
(2015). https://doi.org/10.1109/JSEN.2014.2360039 ISJEAZ 1530-437X Google Scholar
T. Tian, T. Zhang and L. Kong,
“Timeliness constrained task scheduling for multifunction radar network,”
IEEE Sens. J., 19
(2), 525
–534
(2019). https://doi.org/10.1109/JSEN.2018.2878795 ISJEAZ 1530-437X Google Scholar
X. Liu et al.,
“Game model in multi-target imaging task allocation,”
in Asia-Pacific Conf. Syn. Aperture Radar,
1
–5
(2019). https://doi.org/10.1109/APSAR46974.2019.9048276 Google Scholar
S. Li et al.,
“ISAR imaging by two-dimensional convex optimization-based compressive sensing,”
IEEE Sens. J., 16
(19), 7088
–7093
(2016). https://doi.org/10.1109/JSEN.2016.2599540 ISJEAZ 1530-437X Google Scholar
X. Liu et al.,
“Task allocation optimization for multi-target ISAR imaging in radar network,”
IEEE Sens. J., 18
(1), 122
–132
(2018). https://doi.org/10.1109/JSEN.2017.2771804 ISJEAZ 1530-437X Google Scholar
D. Wang et al.,
“Task scheduling for multi-target ISAR imaging in radar network,”
IEEE Access, 8 46092
–46101
(2020). https://doi.org/10.1109/ACCESS.2020.2978904 Google Scholar
Y. Chen et al.,
“An adaptive ISAR-imaging-considered task scheduling algorithm for multi-function phased array radars,”
IEEE Trans. Signal Process., 63
(19), 5096
–5110
(2015). https://doi.org/10.1109/TSP.2015.2449251 ITPRED 1053-587X Google Scholar
J. Chen et al.,
“Multifunction phased radar resource management via maximal pulse interleaving technique,”
Arabian J. Sci. Eng., 38
(11), 3081
–3091
(2013). https://doi.org/10.1007/s13369-013-0617-y Google Scholar
L. Kang et al.,
“3D scattering image reconstruction based on measurement optimization of a radar network,”
Remote Sens. Lett., 11
(7), 697
–706
(2020). https://doi.org/10.1080/2150704X.2020.1757781 Google Scholar
Y. Du et al.,
“Time and aperture resource allocation strategy for multitarget ISAR imaging in a radar network,”
IEEE Sens. J., 20
(6), 3196
–3206
(2020). https://doi.org/10.1109/JSEN.2019.2954711 ISJEAZ 1530-437X Google Scholar
L. Hao, X. Yang and S. Hu,
“Task scheduling of improved time shifting based on genetic algorithm for phased array radar,”
in IEEE Int. Conf. Signal Process.,
1655
–1660
(2016). https://doi.org/10.1109/ICSP.2016.7878109 Google Scholar
L. Huang et al.,
“Task-scheduling scheme based on greedy algorithm in integrated radar and communication systems,”
J. Eng., 2019
(19), 5864
–5867
(2019). https://doi.org/10.1049/joe.2019.0213 Google Scholar
Z. Qu, Z. Ding and P. Moo,
“A machine learning task selection method for radar resource management (poster),”
in Int. Conf. Inf. Fusion,
1
–6
(2019). Google Scholar
BiographyHelei Wang is with the College of Information and Communication Guilin University of Electronic Technology, Guilin, China. Kefei Liao is with the College of Information and Communication Guilin University of Electronic Technology, Guilin, China, also with State and Local Joint Engineering Research Center for Satellite Navigation and Location Service (Guilin University of Electronic Technology), Guilin, China. Shan Ouyang is with the College of Information and Communication Guilin University of Electronic Technology, Guilin, China, also with State and Local Joint Engineering Research Center for Satellite Navigation and Location Service (Guilin University of Electronic Technology), Guilin, China. |