Barrier Coverage Mechanism Using Adaptive Sensing Range for Renewable WSNs

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I. INTRODUCTION
Wireless sensor networks (WSNs) have a wide range of potential applications, including smart home, precision agriculture and environmental monitoring [1], [2]. The coverage is a fundamental issue in wireless sensor networks, which has been widely investigated in recent years. According to different requirements of applications, the coverage problems are classified into target, barrier and area coverage categories [3]. The goal of target coverage is to monitor a number of given targets while the area coverage aims to surveille a given monitoring area. Difference from them, The associate editor coordinating the review of this manuscript and approving it for publication was Guangjie Han . the goal of barrier coverage [4] concerns the border surveillance aiming to detect the intruder's invalid crossing. In the barrier coverage, most studies considered that the boundary region has been deployed a large number of sensors and proposed how to organize the sensors to form the defense lines for detecting illegally crossing a boundary or a protected region. Each independent defense line is referred to a barrier. The barrier coverage is generally applied in very crucial or hazardous circumstance such as military, homeland and critical infrastructure security etc. For ensuring that the constructed barriers can effectively detect illegal crossing of border monitoring area, surveillance quality and lifetime of sensor barriers have been the main focuses of the previous studies. VOLUME 8,2020 This work is licensed under a Creative Commons Attribution 4.0 License. For more information, see https://creativecommons.org/licenses/by/4.0/ The surveillance quality generally depends on a good scheduling mechanism which partitions the sensors into several groups and schedules the sensors in the same group to collaboratively establish the defense barriers. As a key factor of monitoring quality, the sensing ability of each sensor needs to be measured by applying some certain sensing model which directly influences the strategy of scheduling algorithm. There are two sensing models, including Boolean Sensing Model (BSM) and Probabilistic Sensing Model (PSM), often used in literature. A lot of studies [5]- [7] applied BSM which considered the coverage area of each sensor as a perfect disc. That is, each sensor can detect the event if it occurs in the sensing circle of the sensor. These studies aimed to propose scheduling mechanisms to construct defense barriers with k-coverage based on the BSM.
Study [5] identified the critical conditions for strong barrier coverage and proposed a distributed algorithm which partitions the sensors into several groups and schedules different groups working in turn to prolong the network lifetime. Study [6] proposed a self-organized deployment algorithm for mobile sensors aiming to construct k distinct complete barriers to guarantee the k-coverage. Study [7] investigated the issue of how to construct a defense barrier by scheduling a set of sensors for intruder detection. A decentralized algorithm, called BCA, is proposed to construct a maximum number of distinct k-barriers. Though most of these studies constructed the barriers with k-coverage to guarantee a certain level of surveillance quality, the BSM cannot reflect the facts of dynamic changes of sensing range and will reduce the detection accuracy in a real application.
Different from BSM, the PSM assumes that the detecting probability of a sensor is reduced when the distance between the sensor and the target increases. Compared with the BSM, the PSM is more practical, which can reflect the complex sensing effects of the real world. Based on the PSM, study [8] proposed a barrier construction algorithm aiming at minimizing the number of working sensors. The developed algorithm considered the practical functionalities of the real application scenarios and improved the intruder detection probability while reducing the false alarm probability as well. Study [9] considered the directional sensors and applied the PSM as its sensing model. It proposed a barrier construction algorithm which took the collaboration advantages of sensing directions and sensing ranges between neighboring sensors. Study [10] considered a number of parameters which can actually impact the sensing probability. Based on the developed probability sensing model, it proposed sensor placement schemes aiming at achieving the purpose of high coverage and low standard deviations of coverage. Though the abovementioned studies adopted the PSM for achieving better performance, most of the proposed barrier coverage mechanisms did not consider the issue of energy management.
Energy management is another important issue which determines the performance of the barrier coverage. In the past few years, the energy management has received much attention. These studies can be further partitioned into two categories: Energy Conservation (EC) and Energy Harvesting (EH). The schemes of EC aimed to construct more sensor barriers by constructing as many as possible disjoint groups each of which consists of a minimal number of sensors. Different barriers can work in turn, aiming at achieving the purpose of energy conservation. Study [11] developed a learning automata scheme and proposed a distributed algorithm aiming to minimize the number of sensors in each barrier and hence maximize the number of barriers. The different barriers can stay in active mode in turn for the purpose of energy conservation. Study [12] proposed a scheduling algorithm for barrier coverage in heterogeneous sensor networks, aiming at maximizing the network lifetime. They identified several subsets with maximal network lifetime and scheduled them staying in sleep and active states alternatively such that the network lifetime of the constructed barriers can be maximized. Study [13] considered the hybrid sensor network, which consisted of two types of sensor nodes: the energy-scarce ground sensors and the energy-plentiful mobile sensors. Since the energy-scarce ground sensors are static, the goal of this work was to cooperatively reallocate the locations of the mobile sensors for achieving the both purposes of prolonging the network lifetime and improving the surveillance quality of the barrier coverage. Although these studies can increase the network lifetime of sensor barriers, it is inevitable that the battery of the sensors will drain as time goes by. As a result, the wireless sensor network cannot always work for monitoring the boundary region due to its limited network lifetime.
Some other studies considered the Energy Harvesting (EH) scheme to maintain the perpetual network lifetime. They assumed that the sensors are rechargeable for maintaining the perpetual network lifetime. Solar power was considered as one of the most promising environmental energy resources because the scale of sunlight is extensive and easily accessible [14]. The scheduling mechanisms of solarpowered WSNs usually scheduled some sensors staying in active (working) state and keep other sensors in sleeping (recharging) state to achieve the purpose of full coverage while the perpetual lifetime of the WSNs can be maintained. Study [15] discussed target coverage of solar-powered WSNs. An efficient greedy hill-climbing algorithm was developed to orderly switch sensors between recharging and active state, which aimed to maximize the overall surveillance quality of targets. Study [16] presented a reinforcement learningbased sleep scheduling for the solar-powered WSN. Based on the reinforcement learning, the proposed algorithm scheduled the sensor nodes in sleep or wakeup states, aiming to satisfy the desired area coverage. Although the abovementioned scheduling schemes developed for target or area coverage have been developed, the proposed algorithms cannot be applied to the barrier coverage because that the quality of barrier coverage is determined by the barrier with the lowest quality, rather than the total surveillance qualities of the barriers. 86066 VOLUME 8, 2020 Different from studies [15] and [16], study [17] developed the barrier coverage mechanism in solar-powered wireless sensor networks. It proposed a barrier coverage algorithm, called MSQ which allocated the sensor having the largest contribution to monitor the space-time point with the minimal surveillance quality. However, study [17] did not take into account the parameter of variable sensing range which allows the sensing range to be adaptively adjusted.
This paper proposes a Boundary Surveillance mechanism with Adjustable Sensing radius for solar-powered WSNs, called BSAS algorithm. The proposed BSAS is a centralized mechanism and is executed by the sink node. The execution of the BSAS algorithm mainly consists of four phases. In the Space-Time Partitioning Phase, the proposed BSAS firstly divides the boundary curve into several equal-length segments. Similarly, the BSAS partitions the time line into a number of equal length cycles and then partitions each cycle into several equal-length time slots. Herein, we notice that all cycles have identical schedules for every day. Since sensors cannot be recharged in the nighttime, the BSAS considers two types of schedules, including daytime schedule and nighttime schedule. Each sensor stays in either rechargingonly state or sensing & recharging state in each time slot of a daytime cycle. On the other hand, each sensor stays in either sleeping state or sensing-only state in each time slot of a nighttime cycle. In the Contribution Calculation Phase, the BSAS calculates the contribution of each sensor to each space-time point. The contribution of each sensor will be an important reference which will be used for scheduling in the later phase. In the Sensors Scheduling Phase, the BSAS considers the cooperative sensing between neighboring sensors, aiming to schedule all sensors such that the surveillance quality can be maximized while guaranteeing the perpetual lifetime of the WSN. To achieve this, the proposed BSAS treats each segment and time slot as a space-time point, finds the bottleneck points which have the minimal monitoring quality and then schedules as many as possible sensors to work for improving the surveillance qualities of those bottleneck points. Finally, in the Space-Time Transformation Phase, the BSAS dynamically adjusts the sensing radius of some potential sensors aiming to transfer the surveillance quality from space dimension to time dimension such that the monitoring qualities of the bottleneck points can be further improved.
Two main challenges should be overcome when designing the proposed BSAS algorithm. The first one is how to schedule each sensor for achieving the maximal surveillance quality. To cope with this problem, this work tries to identify ''the bottleneck space-time point''. Then, the BSAS schedules as many as possible sensors for improving the surveillance qualities of these points. Another novel scheme, called space-time transformation scheme, for improving the qualities of these points is to dynamically adjust the sensing radius of some sensors. The second challenge is the perpetual lifetime constraint for energy management. Each sensor is continuously recharged in daytime to satisfy the constraint that the recharged energy should be able to support the energy consumption for sensor working in both daytime and nighttime. In other words, the proposed BSAS can ensure sustained survival of sensor barriers. The main contributions of this paper are itemized as follows.
(1) Adopting the weakest-first policy for cooperative sensing. The proposed BSAS algorithm calculates the cooperative sensing contribution of each sensor and identifies the bottleneck space-time point which has the weakest surveillance quality. Then the sensor with the largest contribution to the bottleneck space-time point will be prior scheduled, aiming to maximize the minimal quality of the barrier. In literature, study [15] only considered the schedule of daytime. Therefore, the proposed BSAS algorithm is more practical in real applications. The rest of this paper is organized as follows. Section II presents the network environment and problem statement. Section III gives the detailed descriptions of BSAS algorithm. Section IV presents the simulation results. Finally, a conclusion of the proposed algorithms and future work are drawn. VOLUME 8, 2020

II. NETWORK ENVIRONMENT AND PROBLEM STATEMENT
This section introduces the network environment of the considered WSNs. Then, the objectives and constraints of the investigated problem are described.

A. NETWORK ENVIRONMENT
This paper considers a rectangle region M which contains a boundary curve B. The size of M is L ×W , where L and W are the length and width of M , respectively. Inside the region M , there were n solar-powered sensors S = {s 1 , s 2 , . . . . . . , s n } randomly deployed. The sensing radius of each sensor is identical and adjustable with several fixed levels. The energy consumption of each sensor will increase with its sensing radius. Each sensor is aware of its location. Through beacon exchanges with neighboring sensors, each sensor can collect the IDs, locations as well as remaining energies of its neighboring sensors. Figure 1 gives an example of the considered network scenario.

B. SENSING MODEL
In this paper, the probabilistic sensing model [18] is applied. In general, the target will be detected by the sensor with a higher probability if it is closer to the sensor. Figure 2 shows the probabilities of different sensing regions of the PSM (Probabilistic Sensing Model). Let R = r 1 , r 2 , . . . r q denote the set of q possible sensing radiuses of each sensor, where r i < r j if i < j. When a sensor adopts sensing radius r x for executing monitoring task, there is a safe sensing radius r e x , where r e x < r x . Let A r x denote the area of sensing circle formed by sensing radius r x . The sensing area A r x can be divided into two sub-regions, the safe sensing region A r e x and the unsafe sensing region A r x − A r e x . When an event occurs in the safe region A r e x of a sensor, say s j , the detection probability of this event by sensor s j is 100%. On the contrary, if an event occurs in the unsafe region A r x − A r e x . The detection probability of this event by sensor s j is reduced when the distance between sensor s j and the event happening location is larger.
Let v i denote a given point on a boundary curve. Let s j,x denote sensor s j using sensing radius r x , and use notation s j. * to represent the sensor s j under all sensing radius. Let d s j. * , v i denote the Euclidean distance between sensor s j and point v i . Let p s j,x , v i denote the detection probability of the event happed in point v i by sensor s j with sensing radius r x . The detection probability p s j,x , v i is given by the following Exp. (1).
where λ and γ are the path-loss exponents of the sensing signal strength and could be adjusted with the physical properties of a sensor.

C. RECHARGING AND DISCHARGING MODEL
In the considered wireless sensor networks, all sensors are solar-powered. These sensors have four possible states, including recharging-only state, sensing & recharging state, sensing-only and sleep states. A sensor staying in rechargingonly state or sensing & recharging state can be recharged from the solar energy resource when its power is not full. In sensing & recharging state, the sensors can perform sensing and recharging operations simultaneously. When a sensor stays in sensing & recharging state or sensing-only state, it will perform the monitoring task and hence consume energy. For simplicity, it is assumed that a sensor staying in sleeping state will not consume its remaining energy. In the daytime, the sensors can be recharged and be activated to work. They can stay in either recharging-only state or sensing & recharging state. In the nighttime, all sensors cannot be recharged and can only stay in sleeping or sensing-only states. Assume that the battery capacity of sensors have two levels, including E and E th . The E is maximum capacity of the battery. That is, the initial battery power of all sensors is E. The E th is the threshold of battery power, which is the basic energy required to support the basic operations of each sensor. This also indicates that the available energy for use is bounded by E − E th . Let u sen x denote discharging speed of sensor which adopts sensing radius r x . According to study [19], the discharging speed u sen x can be measured by Exp. (2).
where σ is a constant and t sen x denotes the sensing time period that sensor can continuously perform the sensing operation with sensing radius r x . The value of t sen x can be measured by the Exp. (3).
Recall that the radius set is R = r 1 , . . .r x , . . . r q . The maximum sensing radius of a sensor is r q . When sensing radius is adjusted to r q , the time period for perform sensing operation will be shortest. This time period will be treated as a time slot which is the basic time unit for scheduling. Let notation τ denote a time slot. The value of τ can be calculated by Exp. (4).
Let u chg denote the recharging speed of a sensor and t chg denote the recharging time period. The value of t chg can be calculated by t chg = E − E th u chg . Let notation µ x denote the ratio of recharging and discharging when the sensor adopts sensing radius r x . It is obvious that µ q can be calculated by The solar-powered sensors work intermittently and periodically. A day will be divided into several equal length cycles. Let notation T denote a working cycle of each sensor. A working cycle T consists of several slots in which sensors stay in either sensing & recharging or recharging-only states in the daytime and stay in either sensing-only or sleeping states in the nighttime. The recharged energy in the daytime should be able to support the consumed energy during both daytime and nighttime, because sensors can be recharged only in the daytime. Let L, L daytime and L nighttime denote time lengths of a day, daytime in a day and nighttime in a day. Let ζ −1 denote the ratio of daytime to a whole day. That is, A sensor needs to be recharged for a time period µ q τ in the daytime to support the work of a time-slot τ . We have as shown in Figure. 3. For example, if L daytime = L nighttime , the ζ = 2. The battery of each sensor needs to be recharged for 2µ q τ in one cycle T of daytime, one µ q τ is for sensing work in the cycle of daytime and the other µ q τ is reserved for supporting the sensing work in a cycle of nighttime. Let notation t h denote the h-th time slot in a cycle, where h = 1, 2 . . . , ζ µ q .

D. SENSING RADIUS ADJUSTING MODEL
Recall that R = r 1 , r 2 , . . . r q denotes the set of q possible sensing radiuses of each sensor. If a sensor adopts larger sensing radius, it can contribute higher surveillance quality but consumes more energy, leading to shorter sensing time period t sen x in each cycle. Let δ x denote the ratio between sensing time t sen x and a basic time slot τ , which is represented t sen x = δ x × τ . The fact of τ = t sen q implies δ q = 1. In this model, δ 1 :δ 2 : . . . :δ q−1 :δ q is limited to q:q−1: . . . :2:1. That is According to Exps. (3) and (4), the relation between r x and r q can be derived by applying Exp. (6). Figure 4 gives an example to illustrate the relation between cycle T and sensing radius r x . Assume that q = 3, r 3 = √ 6, ζ = 2 and µ q = 2.5. We can calculate the length of each time slot According to the limitation of sensing radius adjusting model, the time length for sensing in a cycle using three different sensing radiuses are VOLUME 8, 2020 t sen 2 = δ 2 × τ = 2τ and t sen 3 = δ 3 × τ = τ. According to Exp. (6), each sensor has three adjustable sensing radius: r 1 = √ 2, r 2 = √ 3 and r 3 = √ 6. The length of a cycle is T = 2µ q τ = 5τ according to Exp. (5).

E. PROBLEM STATEMENT
This paper presents a scheduling algorithm for the solarpowered sensors which can adjust sensing radius. The proposed scheduling algorithm aims to schedule the sensing radius and the state of each sensor such that the surveillance quality of boundary curve can be maximized. Let a denote one possible scheduling algorithm. The scheduling result applying algorithm a can be represented as a two dimensional matrix D. The value of element D j,h in matrix D represents the scheduling state of sensor s j in the h th time slot. Each sensor can stay at any of the four possible states: sensing & recharging, recharging-only, sensing-only and sleeping state. The element D j,h of matrix D has the following possible value: in sleeping state r x , in other states with radius r x   In the matrix, rows represent sensors and the columns represent time slots. The element D 3,1 = r 1 represents that sensor s 3 is scheduled to stay in sensing & recharging state and its sensing radius adopts r 1 in the 1 th time slot, as shown in Figure 6(a). The element D 1,2 = r 3 represents that sensor s 1 is scheduled to adopt sensing radius r 3 in 2 th time slot, as shown in Figure 6(b). Similarly, the scheduling results of other sensors are given in Figure 6.
The scheduling of each sensor is cycle-based. That is, each sensor has identical schedule in different cycles. This also indicates that the algorithm only needs to schedule each sensor for one cycle. Let S a i,h denote the set of sensors which are scheduled by algorithm a to monitor point v i in the h th time slot. The detection probability p s j,x , v i can be further calculated, according to Exp. (1). In case of s j ∈ S a i,h , the sensing radius r x of s j is recorded in the element D j,h of the scheduling matrix D. Let P a i,h denote the surveillance quality of point v i in the h th time slot by applying scheduling algorithm a. The P a i,h can be calculated by applying Exp. (7).
Given a boundary curve B, the boundary surveillance quality, denoted by U a , is represented by the weakest surveillance quality of all points on boundary curve B. That is, The proposed algorithm aims to achieve the goal of maximal surveillance quality, while guaranteeing the perpetual lifetime of WSNs. Let denote set of all possible scheduling algorithms. The following presents the objective function of this work.
Object Function: Some constraints given below should be further satisfied when developing the scheduling algorithm. Let Boolean notations β sen j,h , β chg j,h and β slp j,h denote whether or not sensor s j performs sensing, recharging and sleeping operations in time slot t h , respectively. That is The following state constraint should be satisfied. Each sensor can only stay in one of the sensing & recharging and sensing-only states at any given time in the daytime, and can only stay in one of recharging-only and sleeping states at any given time at night.
The second constraint guarantees that each scheduled sensor should perform sensing operation for at least one time slot and perform recharging operation for at least one time slot. Let S a denote the set of scheduled sensors by algorithm a. Exp. (11) reflects this requirement.
The third constraint ensures that the total amount of recharged energy is not smaller than that of discharged energy in each scheduling cycle. This constraint guarantees the perpetual lifetime of each sensor. (12) Section III further presents the proposed barrier coverage algorithm which schedules the sensors aiming to achieve the goal depicted in (9), while guaranteeing the satisfactory of constraints (10), (11) and (12).

III. THE PROPOSED SCHEDULING SCHEME
The proposed BSAS algorithm mainly consists of four phases: space-time partitioning phase, contribution calculation phase, sensors scheduling phase and space-time transformation phase. In the first phase, the boundary region is partitioned into several grids such that the boundary curve can be also partitioned into line segments. In addition, this phase also partitions the time line into several equal-length time slots. Through space and time partitions, the two-dimensional space-time points are formed in order to present the surveillance quality of each line segment of boundary curve in each slot. In the second phase, the proposed BSAS calculates the space and time contributions of each sensor. Based on each specific sensing radius, the space contribution of each sensor refers to the coverage qualities of each sensor to the line segments of boundary curve while the time contribution refers to the converge time of each sensor to the line segments of boundary curve. In the third phase, in the sensor scheduling phase, sensors are scheduled to perform recharging or cooperatively sensing, aiming at achieving the goal of maximum surveillance quality under the constraint of perpetual lifetime. Finally, the BSAS dynamically adjusts the sensing radius of some potential sensors aiming to transfer the surveillance quality from space dimension to time dimension such that the surveillance qualities of the bottleneck points can be further improved.

A. SPACE-TIME PARTITIONING PHASE
This phase consists of two tasks: space and time partitioning tasks. The following describes details of the two tasks.

TASK I: SPACE PARTITIONING TASK
In order to reduce the computational complexity, the Space Partitioning Task initially partitions the boundary curve into several line segments. Then the calculation complexity of coverage quality can be transformed from infinite number of points to the fixed number of line segments. The space partitioning task partitions the rectangular areas M into several equal-sized grids. Hence, the boundary curve B in rectangular region M can be further partitioned by these grids. The grids which are passed by the boundary curve can be labeled with an ordered ID from left to right, denoted by G = {g 1 , g 2 , . . . , g m } . A larger grid size can reduce the computational complexity but reduce the calculation accuracy of coverage quality. In the proposed BSAS algorithm, the edge length of each grid is set by 1 √ 2 r 1 where r 1 is the minimum radius in radius set R. This grid size should ensure that any sensor falling in the grid can cover the entire grid, as shown in Figure 7. Let l k denote each line segment where k denotes the number ordered from left to right. Therefore, the boundary curve B can be represented as the set of line segments. That is, we have B = {l 1 , l 2 , . . . , l m }.

TASK I: SPACE CONTRIBUTION CALCULATION TASK
Assume that sensor s j covers line segment l k . The space contribution of sensor s j to line segment l k refers to the coverage quality of line segment l k contributed from sensor s j . Recall that this paper applies the probability sensing model given in Exp. (1). Therefore, one important feature which impacts the space contribution is the distance between sensor s j and line segment l k . That is, a shorter distance between sensor s j and line segment l k can result in larger space contribution of s j to l k . Another important feature which impacts the space contribution is the sensing radius. That is, sensor s j adopting larger sensing radius can increase the space contribution of line segment l k . Let c space j,x,k denote the space contribution of sensor s j to line segment l k at sensing radius r x . Let p s j,x , l k denote sensing probability of sensor s j to line segments l k . The space contribution of sensor s j to line segments l k is measured by sensing probability p s j,x , l k . Without losing fairness, the farthest point on line segment l k from sensor s j is used to calculate p s j,x , l k , as shown in Figure 9.
We have, and Let C space j denote the space contributions of sensor s j provided to boundary curve. The C space j is the space contribution set of sensor s j to all line segments covered by s j under sensing radius r x . That is In this task, the space contribution c space j,k,x of sensor s j to line segment l k should be calculated for each sensor s j ∈ S.

TASK II: TIME CONTRIBUTION CALCULATION TASK
The time contribution of sensor s j to boundary curve refers to the number of time slots that sensor s j can cover boundary curve in a cycle. According to the sensing radius adjusting model, sensors using different sensing radiuses can result in different sensing time. It is obvious that sensors using a smaller sensing radius can consume less energy, leading to longer sensing time in a cycle. According to Exp. (6), the variable δ x which is a ratio of sensing time t sen x and a time slot τ can be calculated based on sensing radius r x . That is, we can obtain the length of t sen x , which is δ x τ . The sink node will evaluate the time contribution of each sensor s j by calculating the sensing time t sen x for each sensing radius r x in a cycle. Let c time j,x denote time contribution of sensor s j to boundary curve when the sensing radius is set at r x . The time contribution c time j,x is in each cycle T = t 1 , . . . , t h , . . . t ζ u q . Let C time j denote the set of time contributions that sensor s j can provide to the boundary curve. We have The following considers an example as shown in Figure 10. There are five sensors s 1 , s 2 , s 3 , s 4 , s 5 and two line segments l 1 and l 2 . The characteristics of sensors in sensing radiuses, recharging rate and discharging rate are similar as those in Figure 4.
The space contributions of sensors s 1 , s 2 , s 3 and s 4 are calculated by Exp. (16). The time contributions of s 1 , s 2 , s 3 and s 4 are calculated by Exp. (18). The Figure 11 depicts the results of contribution calculation.
Until now, the space and time contributions of each sensor s j to each line segment l k covered by s j have calculated. 86072 VOLUME 8, 2020 The next phase aims to schedule sensors such that the surveillance quality of the boundary curve can maximize.

C. SENSORS SCHEDULING PHASE
The major goal of this phase is to schedule the deployed sensors for achieving the maximal monitoring quality. The idea behind the proposed algorithm is to schedule the proper sensors to monitor the space-time point with the least surveillance quality. These points are called bottleneck space-time points. However, the constraints given in Exps. (10), (11) and (12) should be satisfied.
The proposed BSAS mechanism is cycle-based. This indicates that all cycles should have the same schedule. Hence, the scheduling mechanism only pays attention to all spacetime points in one cycle. This phase is further partitioned into two tasks. The first task evaluates the surveillance quality of each space-time point and then finds the bottleneck points. The second task aims to schedule the proper sensors for improving the bottleneck space-time points. To achieve this, the dynamic adjustment of sensing radius is proposed. In what follows, the details of the proposed two tasks are presented.

TASK I: IDENTIFICATION OF THE ''BOTTLENECK POINTS''
Let S c denote set of sensors which can cover the boundary curve. That is Similarly, letS c denote set of sensors which are unable to cover boundary curve. We have, The deployed sensors around boundary curve are divided into two disjoint sensor sets S c andS c . The following schedule calculation only considers sensors in set S c . The process of scheduling sensors in set S c is divided into two categories: unscheduled sensors and scheduled sensors. for obtaining the maximum surveillance quality of boundary curve. In order to know the sensors scheduled in each spacetime point, the sink node will establish a matrix to store the sensor set S sch k,h . Let denote the sensor-scheduling matrix, as shown in Figure 12. Each element [k, h] stores the scheduled sensor set S sch k,h . A row element in the matrix , expressed as S sch k, * , is a set of sensors which have been scheduled to take care segment l k . A column element in the matrix , expressed as S sch * ,h , is a set of sensors which have been scheduled in time-slot t h .
Let u k,h denote the surveillance quality of space-time point α k,h . The value of u k,h is determined by the cooperative detection probability from each sensor s j.x ∈ S sch k,h . We have The sink will establish another matrix to store the surveillance quality of each space-time point, which is expressed as U , as shown in Figure 13.
The proposed scheduling algorithm aims to improve the surveillance quality of each ak ,h . In the following, the line segment lk and time-slot th of bottleneck time-space point is called as bottleneck line segment and bottleneck time-slot, respectively. In the process of scheduling, the number of bottleneck space-time points might be larger than one. Let A wst denote set of bottleneck space-time points. Initially, no sensors are scheduled. That is, VOLUME 8, 2020 surveillance quality of each space-time point is zero. We have In this initial stage, all space-time points are bottleneck spacetime points which belong to set A wst . The next task aims to select sensors in S unsch and schedule them for improving the surveillance qualities.

TASK II: SCHEDULING SENSORS BASED ON ''BOTTLENECK POINTS''
This task aims to schedule all sensors in set S unsch for improving the surveillance quality. To achieve this, three policies are applied: (1) The sensors that can take care of the bottleneck spacetime points in set A wst should be scheduled first. (2) The sensor that has the farthest distance to the boundary curve should be scheduled first. This policy allows all sensors in set S unsch to have opportunities to contribute their coverage to the boundary curve. (3) The farthest sensor adopts the maximal sensing radius r q to maximize its space contribution. Let S b denote the set of sensors that can cover a bottleneck line lk and is unscheduled. That is Up to now, the BSAS schedules sensor s far j,q in time-slot tĥ for helping bottleneck space-time point ak ,ĥ . Next, the sensor set S unsch will be updated as shown in the following.  Continuously consider the example given in Figure 10. Figure 14 shows the initial values of the matrix , U , and set S unsch .
No sensors are scheduled. All space-time points are bottleneck points in set A wst because each u k,h = 0. The first farthest sensor s 1. * from boundary curve is selected to improve the surveillance quality of bottleneck space-time point a 1,1 . Then, the matrix , U and set S unsch are updated, as shown in Figure 15. After the execution of this round, the new bottleneck space-time points in set A wst are formed. The space-time a 1,1 is no longer a bottleneck space-time. In second round, all space-time points are in A wst except a 1,1 . All sensors in the set S unsch are sensors that can help the bottleneck space-time points. The farthest sensor from the boundary curve in set S unsch is s 5. * . The sensor s 5.3 will help bottleneck space-time point a 2,2 according to Exps. (24) and (25). The Figure 16 shows the scheduling result of second round.  Figure 17 shows the scheduling result of the last round. The five sensors in set S unsch are finally scheduled.

D. SPACE-TIME TRANSFORMATION PHASE
This task aims to locally adjust the scheduled sensors such that the surveillance quality of boundary curve can be further enhanced. The key idea is to transfer the space contribution to time contribution for a scheduled sensor, aiming to improve the weakest bottleneck space-time point. To achieve this, a scheduled sensor can reduce its sensing radius such that it can reserve more energy to monitor for other bottleneck time slot. This further provides an opportunity to improve the surveillance quality of some bottleneck space-time points remained in set A wst .
Let f st s j.x : S sch * ,h s j.x → S sch * ,h s j.x−1 + S sch * ,h s j.x−1 denote a transformation function from space to time applied to sensor s j.x . In function f st s j.x , the S sch * ,h s j.x denotes the set of sensors scheduled in time-slot t h and sensor s j.x is in set S sch * ,h . Since sensor s j.x reduces its sensing range from r x to r x−1 , FIGURE 18. Sensor s 1 adjusts its sensing radius from r 3 to r 2 , reducing its space contribution but increasing its time contribution from time slot t h=2 to time slots t h=2 and th =4 . it reserves more energy to perform monitoring task in another bottleneck time-slot th. Therefore, in addition to the original time-slot t h , the new time-slot th is also taken care by sensor s j,  Figure 18 gives an example that the proposed BSAS aims to adjust the schedule of s 1 for improving the surveillance quality of the bottleneck space-time point a 2,4 . Assume that sensor s 1 can cover line segment l 2 . The proposed BSAS applies f st 1,3 function to transfer S sch k=2,h=2 s 1,3 to S sch k=2,h=2 s 1,2 and S sch k=2,h=4 s 1,2 . That is, sensor s 1 reduces its sensing radius from r 3 to r 2 , which transforms its space contribution to the time contribution, additionally performing the sensing operation at slot th= t 4    . The bottleneck space-time points in A wst are also recalculated. The next round of Task III will again be applied until S adj = ∅. That is to say, Task III will be finished if there is no adjustable sensor which can help bottleneck space-time points.
Continuously consider the example given in Figure 17. The bottleneck space-time point is a 2,1 . According to Non-Bottleneck Pre-Condition Property, the adjustable sensor is in set S sch 2,2 = s 5,3 , S sch 2,3 = s 2,3 , S sch 2,4 = s 3,3 or S sch 2,5 = s 4,3 . Take s 2,3 as an example. When its sensing radius is reduced to r 2 , it satisfies the helpfulness property. That is, it has space contribution to bottleneck line segment l 2 since it satisfies condition c space 2,2,2 > 0. The sensor s 2,3 has be scheduled in time-slot t 3 . In time-slot t 3 , the monitoring qualities u 2,2 1,3 = 0.4 and u 2,2 2,3 = 0.3 are still higher than U bef = 0 after adjusting s 2,3 into s 2,2 . That is to say, sensor s 2,3 satisfies Non-Bottleneck Post-Condition Property. The sensor s 2,3 is included in set S adj . The similar calculations can be applied such that the sensor s 5,3 is also included in set S adj . Hence, we have S adj = s 2,3 , s 5,3 . According to Exp. (28), the sensor that performs the space-time transformation in this round is s 2,3 because its space contribution c space 2,3,2 to bottleneck line segment l 2 is greater than c space 5,3,2 of the sensor s 5,3 . The scheduled result of this round is shown in Figure 19. Figure 20 shows the adjusted result of the second round. The sensor s 5,3 is adjusted to help bottleneck space-time a 2,4 . As shown in Figure 21, the task is terminated in last round because S adj = ∅. No sensor can be adjusted.

IV. SIMULATION
This section measures the performance improvements of the proposed BSAS against the existing Maximizing Surveillance Quality Mechanism (MSQ). The proposed BSAS algorithm has two important steps: scheduling new sensors for bottleneck space-time points and adjusting sensing radius of scheduled sensors for bottleneck space-time points. In the first step, different policies can be employed. There are two policies can be employed: the farthest-first and the nearest-first policies. This paper adopts the farthest-first policy which prior schedules the sensor farthest to the boundary curve, aiming to fully utilize the sensors. The proposed BSAS applying the farthest-first policy is called as BSAS_Far. On the contrary, the proposed BSAS applying the nearest-first policy which prior schedules the nearest sensor is called BSAS_Near. The BSAS_Far and BSAS_Near algorithms are compared in simulation. The existing MSQ only schedules the sensors without adjusting the sensing range. The following firstly presents the simulation model and then discusses the simulation results.

A. SIMULATION MODEL
The simulation parameters are given in Table 1. are randomly deployed in monitoring area. Figure 22 depicts two boundaries of amplitudes 5m and 10m. Each sensor has three types of sensing radius: R 1 , R 2 and R 3 . The relationship between R 1 , R 2 and R 3 is The value of R 3 varies ranging from 5m to 20m. In the experiments, the existing MSQ [17] adopting sensing radiuses R 1 , R 2 and R 3 are called as MSQ_R 1 , MSQ_R 2 and MSQ_R 3 , respectively. The proposed BSAS dynamically adjusts the sensing radius aims to improve the surveillance quality of the bottleneck space-time point. The larger sensing radius can achieve greater space contribution but smaller time contribution.
The communication radius is as long as the twice of the sensing radius. The edge of each grid varies from 2m to 10m. The rates for energy recharging and discharging are 20 units/hour and 80 units/hour, respectively. The number of deployed sensors varies ranging from 200 to 1000 while the grid size varies ranging from 2m to 10m. The amplitude is 10m and sensing radius R 3 is 20m. As shown in Figure 23, a common trend that the surveillance qualities increase with number of sensors. This occurs because more sensors can increase the number of active sensors in each time slot, resulting in higher surveillance qualities. Another trend found in Figure 23 is that the surveillance quality decreased with the grid size. This occurs because that a large grid results in a long line segment, which reduces the number of sensors enabling to fully cover the segment. In comparison, the proposed BSAS algorithms, including BSAS_Far and BSAS_Near, outperform the existing MSQ algorithms, including MSQ_R 3 , MSQ_R 2 and MSQ_R 1 . The existing MSQ algorithms just schedule sensors to take care of bottleneck space-time points. Unlike MSQ algorithm, the proposed BSAS algorithms further dynamically adjust the sensing ranges to improve surveillance quality of bottleneck space-time point. As a result, the proposed BSAS_Far and BSAS_Near algorithms achieve better performance, as compared with the existing MSQ_R 3 , MSQ_R 2 and MSQ_R 1 algorithms.  m and 20m, respectively. The grid size is set at 2m. As shown in Figure 24, a common trend that the surveillance qualities significantly decrease with the amplitude of boundary curve. This occurs because of two reasons. One is that a larger amplitude leads to a large monitoring area where the number of deployed sensors is a constant. This causes that the deployment density of sensors to be small, resulting in a low surveillance quality. Another reason is that a large amplitude of boundary increases the length of boundary curve. As a result, the number of segments is increased, which requires more sensors to maintain the surveillance quality. In comparison, the proposed BSAS_Far achieves the best performance. This occurs because BSAS Far+Adj algorithm employs farthest-first policy, which increases the sensor utilization. The algorithms, including BSAS_Near, MSQ_R 3 , MSQ_R 2 and MSQ_R 1 , schedule sensors based on the largest contribution first policy, which firstly schedule the nearest sensor to be active.  The sensing radius varies ranging from 5m to 25m. The number of sensors is set at 600 and grid size is set at 2m. As shown in Figure 25, a common trend that the surveillance qualities significantly increase with sensing radius. This occurs because that the space contribution of sensors to the boundary curve increases with sensing radius. In comparison, the proposed BSAS algorithms, including BSAS_Far and BSAS_Near, outperform the existing MSQ algorithms, including MSQ_R 3 , MSQ_R 2 and MSQ_R 1 under the same amplitude. This occurs because BSAS algorithms can take complementary advantages of time and space. That is, the proposed BSAS algorithms further adjust sensing radius of some sensors to improve the surveillance quality of the bottleneck space-time points.  Figures 26 (a), (b), (c) and (d), respectively. There are 600 sensors deployed in 20m×200m rectangle monitoring area. The sensing radius of each sensor is 20m. The proposed BASA_Far algorithm steady keep a high surveillance quality without large fluctuation, as compared with the other three compared algorithms. It implies that the proposed BSAS_Far achieves better stability of surveillance qualities. The main reason is that the proposed BSAS_Far adopts space-time transformation operations to further improve the surveillance qualities.    Figures 28 (a) and (b) further observe the surveillance qualities of selected space-time points before and after applying the space-time transformation operations of the proposed BSAS_Far algorithm, respectively. The observed time period includes one cycle which consists of five time slots. There are 11 selected locations of the boundary curve to be observed. As shown in Figure 28 (a), the highest and lowest surveillance qualities are 0.69 and 0.999, respectively. This result is obtained only applying the sensors scheduling phase of the proposed algorithm. Figure 28 (b) depicts the improved surveillance quality after applying the space-time transformation phase of the proposed algorithm. The space-time transformation further adjusts the sensing radius of the scheduled sensors according to the bottleneck space-time points. As a result, the highest and lowest surveillance qualities are 0.814 and 1, respectively. In comparison, the space-time transformation operations, as proposed in task III, further improve 12.4% surveillance quality of the lowest surveillance quality.   Figure 28. The rest are scheduled sensors. The scheduled sensors consist of three types with different sensing radiuses. The sensors working at sensing radius R 1 , R 2 and R 3 are marked with blue, pink and green dots, respectively. The sensors adopting sensing radius R 1 , R 2 and R 3 are active for 3, 2 and 1 time-slots, respectively. Initially, the proposed algorithm schedules sensors with sensing radius R 3 . Then, the sensing radiuses of the sensors, marked with blue and pink colors, are adjusted to R 2 and R 1 in adjusting sensing radius of scheduled sensors phase. As shown in Figure 29, those sensors which are adjusted their sensing radiuses are located close to the boundary curve. This occurs because these sensors originally have larger space contribution and thus can be adjusted to transform the space contribution to time contribution by reducing their sensing radiuses. In other words, the sensors can save energy aiming at increasing the sensing time by reducing their sensing ranges. Figures 30 (a) and (b) further compare the time stability and space stability, respectively, of surveillance quality of the five compared algorithms. Figure 30(a) shows the performance of 11 selected locations, in terms of time stability of surveillance quality, are observed for n = 5 time slots. Let u i,j denote the surveillance quality of the i-th location at the j-th time slot. Let ξ i be the time stability of the i-th location, which can be measured by the following Exp. (29).
A value of ξ i closer to 1 represents that the surveillance qualities of the i-th location are similar (or stable) for n=5 time slots.  In comparison, the proposed BSAS_Far achieves the best performance and almost achieves 1, in terms of time and space stabilities. This occurs because that some sensors are adjusted their sensing range to enhance the qualities of the bottleneck points. This help further balance the surveillance qualities of all space-time points.

V. CONCLUSIONS
This paper presents a centralized barrier coverage algorithm, called BSAS, which schedules the solar-powered sensors aiming at maximizing the surveillance quality of a given boundary curve. The sink schedules sensors by applying the proposed BSAS algorithm and distributes the scheduling results to each sensor node. The proposed BSAS applies the probabilistic sensing model to evaluate the cooperative sensing contribution of each sensor and identify the bottleneck space-time points during the construction process of the barriers. Then the space-time transformation scheme, which adjusts the sensing radiuses of the sensors with the largest quality contribution and then schedules them to monitor those points, aims to maximize the surveillance quality of these bottleneck points. Experimental experiments show that the proposed BSAS outperforms the existing studies in terms of surveillance quality and stability. Future work will further consider the communication protocol to report the emergent events when the constructed barriers detect the intruders. Another work will extend the WSNs to the heterogeneous WSNs which consists of different types of sensors.