Coverage-aware sensor engagement in dense sensor networks.
- SourceAvailable from: arxiv.org[Show abstract] [Hide abstract]
ABSTRACT: Wireless sensor networks (WSNs) are emerging as an effective means for environment monitoring. This paper investigates a strategy for energy efficient monitoring in WSNs that partitions the sensors into covers, and then activates the covers iteratively in a round-robin fashion. This approach takes advantage of the overlap created when many sensors monitor a single area. Our work builds upon previous work in "Power Efficient Organization of Wireless Sensor Networks" by Slijepcevic and Potkonjak, where the model is first formulated. We have designed three approximation algorithms for a variation of the SET K-COVER problem, where the objective is to partition the sensors into covers such that the number of covers that include an area, summed over all areas, is maximized. The first algorithm is randomized and partitions the sensors, in expectation, within a fraction 1 - 1/e (~.63) of the optimum. We present two other deterministic approximation algorithms. One is a distributed greedy algorithm with a 1/2 approximation ratio and the other is a centralized greedy algorithm with a 1 - 1/e approximation ratio. We show that it is NP-Complete to guarantee better than 15/16 of the optimal coverage, indicating that all three algorithms perform well with respect to the best approximation algorithm possible. Simulations indicate that in practice, the deterministic algorithms perform far above their worst case bounds, consistently covering more than 72% of what is covered by an optimum solution. Simulations also indicate that the increase in longevity is proportional to the amount of overlap amongst the sensors. The algorithms are fast, easy to use, and according to simulations, significantly increase the longevity of sensor networks. The randomized algorithm in particular seems quite practical.12/2003;
Conference Paper: Exposure in wireless Ad-Hoc sensor networks.[Show abstract] [Hide abstract]
ABSTRACT: Wireless ad-hoc sensor networks will provide one of the missing connections between the Internet and the physical world. One of the fundamental problems in sensor networks is the calculation of coverage. Exposure is directly related to coverage in that it is a measure of how well an object, moving on an arbitrary path, can be observed by the sensor network over a period of time. In addition to the informal definition, we formally define exposure and study its properties. We have developed an efficient and effective algorithm for exposure calculation in sensor networks, specifically for finding minimal exposure paths. The minimal exposure path provides valuable information about the worst case exposure-based coverage in sensor networks. The algorithm works for any given distribution of sensors, sensor and intensity models, and characteristics of the network. It provides an unbounded level of accuracy as a function of run time and storage. We provide an extensive collection of experimental results and study the scaling behavior of exposure and the proposed algorithm for its calculation.Proceedings of the 7th annual international conference on Mobile computing and networking; 01/2001
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ABSTRACT: For many sensor network applications such as military surveillance, it is necessary to provide full sensing coverage to a security-sensitive area while at the same time minimize energy consumption and extend system life by leveraging the redundant deployment of sensor nodes. It is also preferable for the sensor network to provide differentiated surveillance service for various target areas with different degrees of security requirements. In this paper, we propose a differentiated surveillance service for sensor networks based on an adaptable energy-efficient sensing coverage protocol. In the protocol, each node is able to dynamically decide a schedule for itself to guarantee a certain degree of coverage (DOC) with average energy consumption inversely proportional to the node density. Several optimizations and extensions are proposed to provide even better performance. Simulation shows that our protocol accomplishes differentiated surveillance with low energy consumption. It outperforms other state-of-art schemes by as much as 50% reduction in energy consumption and as much as 130% increase in the half-life of the network. Keywords: Sensor Networks, Sensing Coverage, Energy Conservation, Differentiated Surveillance 1.05/2003;
Coverage-Aware Sensor Engagement in Dense Sensor Networks
Jun Lu∗, Lichun Bao and Tatsuya Suda
Bren School of Information and Computer Sciences
University of California, Irvine, CA 92697-3425
Wireless sensor networks are capable of carrying out surveillance missions for various applications
in remote areas without human interventions. An essential issue of sensor networks is to search for the
balance between the limited battery supply and the desired lifetime of network operations. Beside data
communication between sensors, maintaining sufficient surveillance, or sensing coverage, over a target
region by coordination within the network is critical for many sensor networks due to the limited supply
of energy source for each sensor. This paper presents a novel sensor network coverage maintenance
protocol, called Coverage-Aware Sensor Engagement (CASE), to efficiently maintain the required degree
of sensing coverage by turning on a small number of active sensors while putting the others to sleep mode.
Different from other coverage maintenance protocols, CASE schedules active/inactive sensing states of
a sensor according to the sensor’s contribution to the network sensing coverage, therefore preserving
the expected behavior of the sensor network. Coverage contribution of each sensor is quantitatively
measured by a metric called “coverage merit”. By activating sensors with relatively large coverage
merit and deactivating those with small coverage merit, CASE effectively achieves energy conservation
while maintaining sufficient sensor network coverage. We provide simulation results to show that CASE
considerably improves the energy efficiency of coverage maintenance with low communication overhead.
Keywords: Sensor networks, coverage maintenance, sensing coverage, probabilistic sensing model, cover-
∗Corresponding author. Tel.: +1 949 824 4105; Fax: +1 949 824 2886; E-mail: firstname.lastname@example.org
This research is supported by the NSF through grants ANI-0083074, ANI-9903427 and ANI-0508506, by DARPA through
grant MDA972-99-1-0007, by AFOSR through grant MURI F49620-00-1-0330, and by grants from the California MICRO and
CoRe programs, Hitachi, Hitachi America, Hitachi CRL, Hitachi SDL, DENSO IT Laboratory, NICT (National Institute of
Communication Technology, Japan), Nippon Telegraph and Telephone (NTT), NTT Docomo, NS Solutions Corporation, Fujitsu
Wireless sensor networks are networks of a large number of small wireless sensor devices, collaborating to
monitor a target region and report sensing data via wireless channels. Recent wireless sensor networks have
played critical roles in a variety of applications. For instance, thermal sensors are being deployed to monitor
temperature in a forest, and to report the temperature information back to data collection nodes for further
analysis. In another instance, a large number of seismic sensors are employed to monitor animal activities
in a wild field. The seismic sensors, when triggered by animal movements, record the vibration signals and
report them to data collection nodes. Information about animal activities, like their moving tracks and
velocities, can be acquired through analyzing the collected signals.
Except for their convenience in deployments, wireless sensors are very limited in almost every aspect of
their capabilities, such as processing, computing and communication as well as storage and power supply.
For example, the typical Crossbow MICA2 mote MPR400CB  has a low-speed 16MHz microcontroller
equipped with only 128KB flash and 4KB EEPROM. Powered by two AA batteries, it has a maximal data
rate of 38.4KBaud and a transmission range of about 150m. In order to extend the lifetime as well as
improve the reliability of a wireless sensor network, wireless sensors are usually deployed in high density over
a large area and in an ad hoc manner due to the difficulty of manual deployment.
Given such a randomly and densely deployed wireless sensor network, it is desirable to have sensors
autonomously schedule their duty cycles according to local information while satisfying global network
connectivity and sensing coverage requirements. In this paper, we propose a new coverage maintenance
scheme called Coverage-Aware Sensor Engagement (CASE) to efficiently provide required sensing coverage
by activating a small number of sensors while putting the others to sleep. CASE is based on a probabilistic
sensing model, which is closer to the reality than the boolean sensing model assumed by many others. The
boolean sensing model fixes the sensing range of a sensor, while the probabilistic sensing model denotes
sensors’ sensing ability as the probability to detect an event at a location.
Like many other coverage maintenance schemes, CASE targets the K-coverage problem, i.e., to minimize
the number of sensors while guaranteeing any location in the target area is covered by at least K sensors. To
our best knowledge, this work is the first of it kind to address the K-coverage problem under the probabilistic
sensing model. In fact, CASE works for the boolean sensing model as well because the boolean sensing model
is equivalently a special case of the probabilistic sensing model.
CASE works in the following fashion: initially, each sensor is inactive in sensing, but computes its
contribution to sensing coverage, which we called the coverage merit, and see whether it is necessary to turn
on its sensing unit to meet the required degree of sensing coverage. In addition, before turning on itself,
each sensor waits for a back-off period decided by its coverage merit. Sensors with larger coverage merit
have shorter back-off period. In this way, sensors turn on themselves (if necessary) in the decreasing order of
their coverage merit. By utilizing sensors with large coverage merit, CASE can reduce the number of active
sensors needed and therefore conserve the energy consumed to maintain the required degree of coverage.
The other issue, connectivity maintenance, is not considered in this paper. A real sensor network deploy-
ment may have separate requirements on coverage and connectivity. For instance, an application may require
low-quality monitoring but high-bandwidth data transmission, or high-quality monitoring but low-bandwidth
data transmission. Furthermore, sensors may have various combinations of sensing and communication ca-
pabilities. For instance, a sensor’s communication range may be larger or smaller than its sensing range.
The above observations imply that the necessary sensor densities to fulfill the coverage and connectivity
requirements may be different. Thus, it is necessary to separate the control of RF units (i.e., connectivity
maintenance) from the management of sensing units (i.e., coverage maintenance). The connectivity mainte-
nance scheme decides the active/inactive state of RF units and the coverage maintenance scheme determines
the active/inactive state of sensing units. A sensor’s state is represented by the joint state of the RF and
sensing unit. In this way, CASE can be integrated with a connectivity maintenance scheme to fulfill the
application requirements on both coverage and connectivity.
The rest of this paper is organized as follows. Section 2 describes the assumptions of CASE. Section 3
specifies CASE in more details. The differences between our work and the others are examined in Section 4.
Simulation results are presented in Section 5 for performance evaluations. Enhancement and extensions are
discussed in Section 6. Section 7 presents related work and section 8 concludes the paper.
2 Sensor Network Assumptions
We assume that sensors are static and location-aware. Such assumptions are also reasonably taken by other
related work on sensor network coverage (e.g.,   and ), and supported by the existing work on the
localization problem (e.g.,    and ). Only the location information of a sensor’s neighborhood
in twice sensing range is required at each sensor. We also require that sensors are synchronized, which can
be obtained through the existing research (e.g.,  and ).
We assume probabilistic sensing model of sensors. Due to signal attenuation and noise disruptions, a
sensor’s measurement of an event follows a probability density function varying with the type of signals
and the propagation environment. A successful detection of an event depends on the quality of the sensor
measurement. We call the probability of a successful detection as the sensing ability of a sensor.
The sensing ability model of a sensor is measured through a calibration process before deployment. We
use Si(p) to denote sensor i’s sensing ability at location point p. Apparently, Si(p) is a function of the
distance between sensor i and location p . A sensor’s sensing range, denoted by SR, is defined as the
distance from the sensor, beyond which the sensor’s sensing ability is negligible. The boolean sensing model
is regarded as a special case of the probabilistic sensing model, where a sensor detects an event within the
SR with probability 1, and beyond the SR with probability 0.
For clarity of algorithm discussion, we further assume that sensors’ communication range, denoted by CR,
is at least twice SR. This assumption is usually true for real sensors. For example, HMC1002 megnetometer
sensors have the SR of approximately 5m  while the CR of MICA2 MPR400CB mote is about 150m .
In the case that the CR is less than twice SR, CASE still works by propagating control beacons through
3Coverage-Aware Sensor Engagement (CASE) Specification
3.1 K-Coverage Maintenance
Sensor coverage represents the quality of surveillance provided by a sensor network, which could be defined
in various ways. CASE targets the classic K-coverage maintenance problem motivated by the intrusion
detection application. For intrusion detection applications, a minimal number of detecting sensors is usually
required in order to localize the intruder. To be consistent with the K-coverage definition, we define the
sensing coverage to a location as the number of sensors covering a location.
Definition 3.1 Coverage (Probabilistic Sensing Model) - Given a sensor group A, the coverage offered by
A to a location point p is denoted by CA(p), which is defined as the expected number of the sensors covering
p, or the weighted sum of covering sensors, as shown in Eq. (1).
where Si(p) is the sensing ability, or the probability of sensor i to detect an event at location point p.
Location point p is said to be K-covered by A if CA(p) is at least K and a region is K-covered if any location
point within the region is K-covered.
CASE solves the K-Coverage Maintenance problem defined as the following.
Definition 3.2 K-Coverage Maintenance - Given a sensor group A deployed in region R and a real number
K, choose a subset A?such that
∀p ∈ R |
CA?(p) ≥ K,
CA?(p) = CA(p),
CA(p) ≥ K
CA(p) < K
where CA(p) and CA?(p) denote the coverage to the location point p offered by A and A?, respectively.
Note that the required coverage degree K can be a real number under the probabilistic sensing model. For
example, an application may require the target region to be 1.5-covered, which means the expected number
of sensors that detect an event at any location within the area should be at least 1.5.
When location point p is covered by a sensor group A, the additional coverage needed to fulfill the K-coverage
requirement at point p is
m∈ASm(p), K >?
Note that when?
coverage needed for this location is 0. In order to measure sensor i’s contribution to fulfill K-coverage at
m∈ASm(p) is greater than or equal to K, p is already K-covered, therefore the additional
location point p, we define a sensor’s coverage merit.
Definition 3.3 Sensor i’s coverage merit at location point p is defined as the minimum of its sensing ability
and the additional coverage needed to fulfill the K-coverage requirement at p, or
CMi(p) = min(Cadd(p),Si(p))(3)
Definition 3.4 Sensor i’s coverage merit CMi evaluates the sensor’s contribution to the sensor network
coverage as a whole, which is computed as the integration of CMi(p) over the entire target area, i.e.
Since the existence of a sensor only affects the area covered by the sensor, its coverage merit can be calculated
by only considering the area within its SR. For computation convenience, the above equation is transformed
into polar coordinates:
The concept of coverage merit defined under the probabilistic sensing model is also applicable for the boolean
sensing model. As we described, the boolean sensing model can be regarded as a special case of the prob-
abilistic sensing model, under which a sensor detects an event within the SR with the probability 1 and
beyond the SR with the probability 0. Thus, Eq. (2) can be transformed to
K − |A|,
K > |A|
K ≤ |A|
where |A| means the number of sensors in group A. Accordingly, we have
1, K > |A|
0,K ≤ |A|
where p is a location within the SR of sensor i. Therefore, the coverage merit of a sensor defined by Eq. (4)
actually means the portion of the sensing area that is not K-covered. For example, in Fig. 1, sensor i in
the middle is surrounded by three active neighbors. The acreage of the gray portions in Fig. 1(a) and 1(b)
shows the coverage merit of sensor i to maintain 1-Coverage and 2-Coverage, respectively.
3.3 Scheme Description
To minimize the number of active sensors to provide K-coverage, CASE adopts a greedy strategy by gradually
activating sensors in decreasing order of their coverage merit. That is, CASE always prefers to employ sensors
with relatively large coverage merit to provide coverage. In contrast, previous schemes schedule sensors purely
based on their sensing redundancy, regardless of their influence on fulfilling the required degree of coverage.
More specifically, time is slotted into rounds and CASE goes through two phases at the beginning of each
1. Wakeup phase: the first phase when sensors start in inactive state, and if necessary, gradually enter
the active state according to their coverage merit.
2. Optimization phase: the second phase when sensors optimize the coverage by turning off redundant
sensors to meet coverage requirements.
In the wakeup phase, each sensor is inactive in sensing and keeps an active neighbor list initialized to
empty. The active neighbor list stores the IDs and coordinates of active neighbors. Sensors keep their RF
units on as they need to exchange control beacons with neighbors.
Each sensor computes an initial coverage merit using the active neighbor list. According to Eq. (2),
with an empty active neighbor list, the additional coverage needed for any location is K. Thus, the initial
coverage merit of a sensor is maximum, as given by Eq. (5).
Afterward, each sensor sets a back-off timer T to transit to active state and announce its active state. The
back-off timer T is determined according to its coverage merit using Eq. (6).
T = ξ · (CMmax− CM) + ?
where CM is the current coverage merit calculated by the sensor, ξ is a configurable system parameter, and
? is a small positive random number. ξ determines the convergence latency of the wakeup phase in CASE.
Small value of ξ means fast convergence but may increase the chance of collisions among neighboring sensors.
The choice of an appropriate value for ξ is out of the scope of this paper, and will be part of our future work.
The random term ? is introduced to break ties in the case that multiple neighboring sensors have the same
coverage merit (e.g., every sensor has the same maximal coverage merit at the beginning).
When a sensor times out, the sensor enters active state, and broadcasts a TURNON message with its ID
and coordinates to the neighbors within CR, which is approximated by twice SR. When a neighbor receives
a TURNON message before the timer expires, it adds the sensor to the active neighbor list, recalculates the
coverage merit, and adjusts its back-off timer accordingly.
Eq. (6) tells that sensors with larger coverage merit have shorter back-off period. Therefore, sensors
with more contribution to sensing coverage time out earlier and become active, which in turn, reduces the
coverage contribution of neighboring sensors that are still in back-off period. As the result, the neighboring
sensors re-schedule their back-off timers according to the new coverage merit value. Since the coverage merit
always decreases with more active neighbors, the back-off timer is always delayed. Once a sensor’s coverage
merit decreases to 0, the sensor cancels its back-off timer and stays inactive. The wakeup phase ends at
around ξ · CMmax.
The wakeup phase, however, may produce redundant active sensors because the coverage of the sensors
turning on later may overlap with the sensing areas of the sensors that are already active. One example is
shown in Fig. 2. To cover the rectangle target area, sensor i times out before sensor x, y and z. Since none
of the sensors is redundant when timing out, all the four sensors turn into active state. However, sensor i is
redundant in the resulted network.
Right after the wakeup phase, each active sensor goes through the optimization phase, using a simple
random back-off procedure to turn off redundant sensors generated in the wakeup phase. Accordingly, each
active sensor calculates its coverage merit to check its redundancy. Each redundant sensor sets a random
timer before turning off. Upon timing out, a sensor re-checks its redundancy and turns off accordingly. If a
sensor turns off, it broadcasts a TURNOFF message with its ID to inform its neighbors. Neighbors receiving
such a message remove the sensor from their active neighbor lists so that the sensor will not be counted to
decide their redundancy later.
The CASE is again specified with pseudo codes and state transition graph in Fig. 3 and Fig. 4, respectively.
Note that only the wakeup phase algorithm is illustrated.
4Comparisons with Prior Work
To our best knowledge, CASE is the first to address the K-coverage under the probabilistic sensing model.
Existing work cannot be applied directly to probabilistic sensing model. For example, the eligibility rules
proposed in  and  are not valid for probabilistic sensing model.
Tian and Georganas  proposed a simple scheduling algorithm, in which every sensor decides its
redundancy through checking whether its sensing area is contained in the union of the sponsored sectors
offered by its neighbors within SR. For example, the shadowed region in Fig. 5(a) means the sponsored
sector offered by sensor j to i. Sensor i in Fig. 5(b) is redundant since its sensing region is fully covered by
the union of the sponsored sectors offered by its three neighbors. A back-off mechanism is used to avoid blind
points caused by simultaneous decisions of multiple sensors. After the back-off period, a sensor eligible to
turn off broadcasts a TURNOFF beacon to inform its neighbors within SR. Upon receiving the TURNOFF
beacon, neighboring sensors remove the sensor from the neighbor list so that the sensor will not be counted
to decide the eligibility of other sensors. Obviously, the native scheduling algorithm proposed in  does
not work for the probabilistic sensing model.
In order to evaluate the performance of CASE, we modified the eligibility rule of the scheme presented
in  so that it can be applied to probabilistic sensing model, and compared the modified scheme with
CASE. We choose the scheme proposed by  because of its simplicity and easiness to be adapted to the
probabilistic sensing model. For some other coverage maintenance schemes, such as the ones proposed in
 and , their scheme design is tightly coupled with the assumption of boolean sensing model, and
thus cannot be adapted to the probabilistic sensing model. We refer the native scheme proposed in  as
the sponsored sector scheduling scheme or Tian-Sector and the scheme modified as the grid point scheduling
scheme or Tian-Grid. In Tian-Grid, the target area is covered by a virtual square grid as shown in Fig. 6
and sensors only check the expected number of monitoring sensors at each grid point within its SR in order
to decide its redundancy. A sensor is redundant and thus eligible to turn off if the expected number of
monitoring sensors of each grid point within its SR is at least K. The same back-off mechanism as Tian-
Sector is used to avoid blind points caused by simultaneous decisions of multiple sensors. Different from
Tian-Sector, which only examines the sectors sponsored by neighbors within SR, Tian-Grid considers all the
neighbors within twice SR. Tian-Grid provides an approximation of K-coverage over the entire area since
it only guarantees coverage on the grid points.
There are two major differences between CASE and Tian-Grid. First, CASE differentiates sensors ac-
cording to their coverage merit, which reduces the active sensor density needed to provide the required degree
of coverage. Second, unlike Tian-Grid, which tries to turn off redundant sensors, CASE only turns on sensors
that are necessary to provide the required degree of coverage. This feature is favorable for dense deployment
in that the communication and computation overhead is confined due to limited sensor state changes.
Note that both CASE and Tian-Grid can work under the boolean sensing model by treating the boolean
sensing model as a special case of the probabilistic model. In Section 5, we will compare their performance
under both models through simulations.
5.1 Simulation Setup
We carried out simulation experiments under two types of sensing models — the probabilistic sensing model
and the boolean sensing model, both to cover a square area of 100×100m2.
ξ and ? of Eq. (6) are set to 0.1 and 0.01, respectively. If not explicitly specified, the deployment density
is set to 0.08sensors/m2and the required degree of coverage is set to 1.0.
The probabilistic sensing models depend on the sensor capabilities and environments. Although CASE
shall work with any realistic sensing model, for simplicity, we assume a virtual probabilistic sensing model
for the sensors, two examples of which are shown below,
Si(p) = f(dip) =
ip+ ··· + γdk
1 + αdip+ βd2
Si(p) = f(dip) =
where dipis the distance between sensor i and location p; α, β, γ and χ(α, β and γ ≥ 0, χ > 1) are system
parameters reflecting the physical characteristics of sensor i and deployment environments.
Specifically, we assume the following virtual probabilistic sensing model in the simulations:
(1 + αdip)β
where α is set to 0.1 and β is set to 3 or 4. Assuming that detection probability lower than 4% is negligible,
two SRs, i.e.,15m and 20m, are simulated. For the boolean sensing model, the SR is fixed at 15m.
5.2 Result Analysis
The simulation results show the performance of CASE in terms of active sensor density, communication
overhead and the distribution of sensing coverage. The communication overhead is computed as the number
of beacons sent and received for the TURNON messages in the wakeup phase and the TURNOFF messages in the
We analyze the results under the probabilistic sensing model and the boolean sensing model separately.
5.2.1Probabilistic sensing model
For comparison purposes, we simulate the modified Tian-Sector protocol, which we refer as Tian-Grid in the
figures. The probabilistic sensing model described in Eq. ( 7) is assumed and two sets of parameters are
adopted (i.e., α set to 0.1, β set to 3, SR set to 15m, and α set to 0.1, β set to 4, SR set to 20m).
Fig. 7 shows the active sensor density to fulfill the required degree of coverage by varying sensor deploy-
ment density (Fig. 7(a)) and the required degree of coverage(Fig. 7(b)). Fig. 7(a) indicates that both CASE
and Tian-Grid provide stable active sensor density under different sensor deployment density. However,
CASE results in lower active sensor density than Tian-Grid because CASE activates sensors with large cov-
erage merit, therefore employing fewer active sensors to achieve the same degree of coverage. For instance,
when the sensor network has the deployment density of 0.05sensors/m2and sensors have the SR of 20m,
CASE provides 1.0-Coverage with the active sensor density of only 0.0137sensors/m2, whereas Tian-Grid
requires 0.0175sensors/m2. Fig. 7(b) shows the results based on various coverage requirements. Again,
CASE outperforms Tian-Grid for all the cases.
Fig. 8 demonstrates the number of beacons transmitted under different sensor deployment densities and
coverage degrees required. We can see that CASE uses fewer beacons than Tian-Grid. This is due to the
fact that sensors are gradually switched on from inactive state to active state in CASE, whereas Tian-Grid
has all sensors initially in active state and turn off redundant sensors, which translates into different number
of beacons transmitted in order to inform state changes. If the network deployment is dense enough, the
number of redundant sensors is much larger than the number of active sensors needed to provide the required
degree of coverage. Thus, CASE involves fewer state changes than Tian-Grid and, as the result, incurs fewer
beacons transmitted. Furthermore, from Fig. 8(a), we observe that the number of transmitted beacons in
CASE changes little along with the increase of deployment density. This is due to the fact that the active
sensor density is almost stable along with the deployment densities in CASE. In contrast, Tian-Grid suffers
when the deployment density increases because more redundant sensors need to turn off and send more
TURNOFF beacons. Fig. 8(b) shows that CASE incurs more beacons while Tian-Grid causes fewer beacons
with the increase of required degree of coverage. In order to fulfill a greater degree of coverage, more sensors
turn on in CASE while fewer sensors turn off in Tian-Grid. However, compared with sensor deployment
density that could grow to a very large number, the required degree of coverage can be regarded as a limited
Fig. 9 shows the number of beacons received in CASE and Tian-Grid for various sensor deployment
densities and required coverage degrees. Similar to Fig. 8(a), Fig. 9(a) shows that CASE causes fewer
received beacons than Tian-Grid, and that the number of beacons received in both schemes increases with
the deployment density because of the broadcast nature of the wireless channel. However, the increasing
rate of received beacons of CASE is less than that of Tian-Grid. In CASE, the increase is purely caused by
the growth of sensor density. In Tian-Grid, however, the growth of the number of the transmitted beacons
also contributes to the increase of number of beacons received. Actually, detailed analysis of the data yields
that the growth is linear for CASE and quadratic for Tian-Grid. Also, from Fig. 9(b), we have the similar
observation to Fig. 8(b), CASE incurs more beacons while Tian-Grid causes fewer beacons with the increase
of the required degree of coverage.
To further investigate the performance of CASE, we show the probability function of resulted coverage
degrees in Fig. 10(a), for which the required degree of coverage is 1.0. As we can see, with CASE, majority
of the location points are covered by a degree from 1.0 to 2.0, while the coverage of Tian-Grid spreads from
1.0 to 3.0. CASE also presents less mean and variance of coverage than Tian-Grid. We also plotted the
coverage degree of different points in the sensor network as shown in Fig. 10(b), which indicates that CASE
provides smoother coverage than Tian-Grid does.
In CASE, each sensor calculates its coverage merit based on its own and active neighbors’ location. In
practice, however, location measurement is often noisy and incurs error. In Fig. 11, we present the impact
of location error in terms of the percentage of blind point (i.e., the location points that are not K-covered)
out of 10,000 sampling points and the coverage distribution. K is set to 1.0 and the deployment density is
0.08sensors/m2in the tests. Fig. 11(a) shows the percentage of the blind points with different maximum
location error varying from 0 to 15m. We can see that the blind point percentage increases with the location
error and reaches about 20% when the maximal location error is 15m. Fig. 11(b) shows the details of the
coverage distribution. We observe that, with the degradation of location accuracy, the coverage of different
location points becomes more spreading, which means more area is under-covered or over-covered. For
example, in the worst case of maximal location error as 15m, about 98% area is covered between 0.5 and 3.0,
while about 98% area is covered between 0.9 and 2.0 when maximal location error is 5m. This observation
can be easily understood since location error incurs error in coverage merit calculation and may cause sensors
to make poor decisions on sensing states.
5.2.2Boolean sensing model
We compare CASE with Tian-Grid and Tian-Sector under the boolean sensing model as well. In , a
theoretical lower bound on the active sensor density to achieve 1-coverage is provided as 2/(√27SR2), and
is again calculated here as a baseline for the comparison purposes.
Fig. 12(a) shows that Tian-Grid achieves the same required degree of coverage with less than half of
the active sensor density required by Tian-Sector. Because Tian-Sector is conservative about the sensor
redundancy by only considering the neighbors within SR and ignoring the coverage overlapping with the
sensors in the range from SR to 2·SR, Tian-Sector results in relative high density of active sensors. Again,
CASE outperforms Tian-Grid by reducing 20% of the active sensor density. Fig. 12(b) illustrates that CASE
outperforms both Tian-Grid and Tian-Sector to provide various coverage degrees.
A larger discrepancy between CASE and the other two protocols are shown in terms of the communication
overhead in Fig. 13 and 14. For the boolean sensing model, sensors’ sensing ability for the entire sensing area
is constant at 1.0. Thus, with the same sensor deployment density, the boolean sensing model has greater
redundancy than the probabilistic sensing model, which means more sensors need to turn off in Tian-Grid
6 Discussion and Enhancement
The computation overhead incurred by CASE is mainly to calculate coverage merit using Eq.(4), which
involves a double integration. Obviously, there exists a tradeoff between the computation overhead and
the calculation precision. Although from the aspect of energy consumption, computation is not as major as
sensing and communication , complex computation on simple sensors with slow processors can cause long
latency, and as the result, degrades the algorithm performance. Thus, the choice of calculation precision
should be accurate enough to differentiate sensors with different coverage contribution, while not overwhelm-
ing the computation capability of simple sensors. Enhancement to reduce the computation overhead will
improve the performance of CASE in a real deployment.
In CASE, each sensor sets a back-off timer and recalculates its coverage merit each time when receiving a
TUNRON message. Based on the new coverage merit value, it reschedules its timer. According to Eq. (2), (3)
and (4), the sensor’s coverage merit is reduced and the back-off timer is always delayed when a new neighbor
is turned into active state. To further reduce the computation overhead, each sensor, when receiving a
TURNON message, instead of recalculating its coverage merit immediately, only records the TURNON
message. When the back-off timer goes off, the sensor checks whether it received TURNON messages during
the back-off period. In the case that it receives no TURNON message, it simply turns on and broadcasts a
TURNON message. Otherwise, it recalculates the coverage merit and schedules another timer.
Since a sensor may receive more than one TURNON messages during the back-off period, this en-
hancement reduces the computation overhead by merging coverage merit calculations triggered by multiple
messages received in the back-off period. Fig. 15 shows that the enhanced CASE (referred as CASE-II in
the figure) can reduce the computation overhead by more than 75% depending on the deployment density.
Note that the simulation results given in Fig. 15 is for the probabilistic sensing model and similar simulation
result is obtained for boolean sensing model.
In a sensor network application, the required degree of sensing coverage may be different depending on the
locations. For example, in battlefield, the command center should be covered with extra sensors in order
to enhance the reliability and confidence of monitoring. CASE can be easily extended to support such
differentiated surveillance of hot spots. The required degree of coverage and the scope of the hot spot can
be transmitted to the sensors by geographical multicast (e.g., ), so that sensors can easily differentiate the
area within and outside the hot spots. Fig. 16 shows the resulted coverage distribution with the hot spot as
a circle area in the middle of the field with the required degree of coverage set to 2.0 for the hot spot and
1.0 for the remaining area.
The self-organization of sensor networks to maintain global connectivity and coverage has drawn intense
research attention recently. Xing et al.  pointed out that connectivity maintenance and sensing coverage
maintenance are two different but related issues and both are essential for wireless sensor networks.
Extensive work has been done on the connectivity maintenance issue. To list a few examples, the research
in  focuses on energy conservation by controlling sensor transmission power in order to maintain network
connectivity. It demonstrated that the network connectivity can be maintained if each sensor has at least one
neighbor in every cone of 2π/3. In ASCENT , sensors decide whether to join the routing infrastructure
based on the number of active neighbors and message loss. Sensors detecting high message loss can also
send HELP messages to solicit more sensors to join the network. Xu et al.  proposed two algorithms that
can conserve energy by identifying and turning off redundant nodes of connectivity. Geographic Adaptive
Fidelity (GAF) identifies redundant nodes by node physical location and estimating radio range. Cluster-
based Energy Conservation (CEC) determines node redundancy using only connectivity information.
The other issue, coverage maintenance in sensor networks, has also been attracting much research effort
Some of the research approaches the problem from the theoretical perspective. The authors of 
analyzed sensor network coverage of wireless sensor networks by studying the relation between the number
of neighbors and the coverage redundancy. Liu and Towsley  investigated the limits of sensor network
coverage in terms of different coverage measures, i.e., area coverage, node coverage fraction and detectability.
The critical conditions of sensor network configuration for asymptotic coverage are investigated in .
Other research proposes coverage maintenance protocols. Tian and Georganas  presented a node-
scheduling algorithm to turn off redundant sensors if their sensing areas are already covered by their neigh-
bors. Randomized as well as coordinated sleep algorithms were proposed in  to maintain network coverage
using low duty-cycle sensors. The randomized algorithm enables each sensor to independently sleep under
a certain probability. The coordinated sleep algorithm allows each sensor to enter sleep state if its sensing
area is fully contained by the union set of its neighbors. A K-coverage maintenance algorithm was proposed
in  so that each location of the sensing area is covered by at least K sensors. A sensor decides whether it
is redundant only by checking the coverage state of its sensing perimeter. Abrams et al. studied a variant of
the NP-hard SET K-COVER problem in , partitioning the sensors into K covers such that as many areas
are monitored as frequently as possible. Yan et al. proposed an adaptable energy-efficient sensing coverage
protocol, in which each sensor broadcasts a random time reference point, and decides its duty schedule
based on neighbors’ time reference points . Co-Grid proposed in  schedules sensors by adopting a
distributed detection model based on data fusion.
Some research considers the joint problem of connectivity and coverage maintenance. Xing et al. 
studied the relationship between coverage and connectivity, and proposed a coverage maintenance scheme,
called Coverage Configuration Protocol (CCP). CCP is integrated with an existing connectivity maintenance
scheme to provide both coverage and connectivity guarantees. The work presented in  considers a
grid network of unreliable sensors, i.e., sensors can probabilistically fail. It is addressed that connectivity
and coverage can be maintained with high node density, even if each node is highly unreliable and the
transmission power is small. In , each sensor’s communication and sensing activities is modeled as a
Markovian stochastic process. The approach is proposed to minimize the power consumption while ensuring
connectivity and coverage properties. In , the lifetime of a sensor network under the guarantee of both
connectivity and coverage is studied. The lower and upper bound of the network’s maximum lifetime are
presented. In , Zhang and Huo presented a coverage and connectivity maintenance algorithm, which
optimizes coverage configuration by minimizing the sensing overlap among neighboring sensors.
The existing coverage maintenance algorithms, however, assume boolean sensing model and cannot be
directly applied to probabilistic sensing model.
We have proposed a novel coverage maintenance scheme called Coverage-Aware Sensor Engagement (CASE).
CASE conserves energy while providing the required degree of coverage by allowing sensors to autonomously
decide their active/inactive states. Unlike prior works, CASE considers local coverage information of sen-
sors, i.e., coverage merit, when scheduling sensors’ active/inactive states. Simulation results show that
CASE provides the required degree of coverage for a dense sensor network with lower active sensor density.
Furthermore, we demonstrate that CASE is highly scalable to sensor network deployment density in terms
of communication overhead through simulation study.
We would like to thank Yoshiaki Hori at Kyushu University and anonymous reviewers for their valuable
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less sensor networks. In Proceeding of International Conference on Information Processing in Sensor
Networks (IPSN), 2004.
 J. Albowicz, A. Chen, and L. Zhang. Recursive position estimation in sensor networks. In Proceeding
of IEEE International Conference on Network Protocols (ICNP), 2001.
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Proceeding of IEEE INFOCOM, 2000.