A Balanced Energy-Efficient Multihop Clustering Scheme for Wireless ...

A Balanced Energy-Efficient Multihop Clustering Scheme for Wireless Sensor Networks Lina Xu

G.M.P O’Hare

Rem Collier

University College of Dublin, Ireland Email: [email protected]

University College of Dublin, Ireland Email: [email protected]

University College of Dublin, Ireland Email: [email protected]

Abstract—Network lifetime is crucial in Wireless Sensor Network (WSN) systems since recharging or exchanging the sensors is difficult and expensive. Clustering techniques provide an interface for WSN topology management to extend network lifetime. Existing clustering algorithms, such as LEACH and HEED, can significantly reduce the power consumption on each sensor and thus prolong the network lifetime. However, most existing work fails to consider the coverage of the network when evaluating the lifetime of a network. An advanced clustering algorithm should not only be able to extend the longevity, but also maintain the coverage. We believe that evening the load in every unit area rather than on each single sensor can provide betterbalanced power usage through the network. Although it is hard to achieve perfectly balanced load, the sensors that are still alive should be well distributed over the sensing area. In this paper, we propose a novel algorithm based on HEED, named the Balanced Energy-Efficiency (BEE) clustering algorithm. Experimental results show that BEE exceeds HEED and LEACH from two perspectives: 1) longevity and 2) balanced sensor distribution. It can guarantee the network coverage for a longer time, compared with HEED and LEACH. We also illustrate the multihop version of BEE, called the Balanced Energy-Efficiency Multihop (BEEM) clustering algorithm, which can further improve the performance of BEE.

(a) Structure

balance the energy consumption through the network, CH rotation between sensors is necessary. •

Energy aware CH election: High residual energy sensors are elected as CHs to even the power usage.

•

Cluster size: The CH of a big cluster consumes more energy than the CH of a small cluster. To even the cluster size, the CHs should be well distributed in the network. The chance that two sensors in each other’s cluster range both become CHs should be low.

•

Data fusion: To reduce the transmission cost, the CHs can assemble the received data and send the fused data to the BS.

•

Transmission power control (TPC): Through transmission power control, a sensor can communicate with its CH by using the minimal transmission power level while maintaining the transmission quality.

I NTRODUCTION

Owing to the fast development and great advantages of Wireless Sensor Networks (WSNs), corresponding technologies have drawn a lot of attention in different fields, such as battlefield sensing, disaster management, wildlife monitoring, etc [1]. WSNs are normally comprised of thousands of nodes that are embedded with limited energy resources. How to extend the lifetime of such a network is challenging. As a major approach to increasing energy efficiency, clustering techniques provide a smart topology control scheme for WSNs. Clustering algorithms can partition the sensors in a network into different clusters. A sensor in each cluster, elected as Cluster Header (CH), is responsible for creating a transmission schedule, gathering and fusing data and sending data back to the Base Station (BS). Several techniques are used in current clustering algorithms to achieve longer lifetime: •

CH rotation: Since the CHs are in charge of data gathering from the sensors in the clusters, data assembling and data transmission to the BS, they normally consume more energy than other normal sensors. To

c 2014 IEEE 978-1-4799-3060-9/14/$31.00

(c) Simulator

Fig. 1: Statistics of 25 existing clustering algorithms

Keywords—Wireless Sensor Network, energy efficiency, clustering, multihop, balanced distribution.

I.

(b) Control manner

As we can see, all the techniques focus on reducing the energy consumption of each sensor. When evaluating a clustering algorithm, power consumption is normally the only concerned metric, to the detriment of other issues such as network coverage. Network coverage is determined by the distribution and sensing range of the sensors. Normally a certain type sensor has a fixed sensing range. To maintain coverage, the distribution is pivotal. In this paper, we aim to provide a distributed clustering algorithm that can not only extend network lifetime, but also guarantee coverage of the network. The name of our algorithm is Balanced Energy-Efficient Multihop (BEEM) clustering algorithm. To decide the structure and simulation environment, we analyzed 25 papers (including LEACH [2], LEACH-C [3], LEACH-TL [4], HEED [5], EECS [6], EEHC [7] DWEHC [8],

TABLE I: Comparison of 6 Existing Clustering Algorithms and BEE(M). Algorithm

Distributed

LEACH

Cluster Structure Voronoi

CH Rotation Yes

Data Fusion Yes

TPC

Yes

Node Density No

Cluster size No

Sensing Abilities None

Simulation

Yes

Energy Aware No

HEED DWEHC

Voronoi Voronoi

Yes Yes

Yes Yes

Yes Yes

Yes Yes

Yes Yes

Yes Yes

Yes Yes

MATLAB NS-2

Yes

Yes

No

Yes

No

Energy Location Energy Location

PEGASIS

Chain

Yes

No No

Yes

Yes

No

Yes

No

MATLAB

No

No

No

No

No

Yes

No

MATLAB

Direct

Yes

Yes

Yes

Yes

Yes

Yes

Yes

Location Energy Location Energy Energy

Direct LEACH PEGASIS

CCS

Chain

No

S-WEB

Spectrum

BEE(M)

Voronoi

MATLAB

LEACH HEED

PANEL [9], UCS [10], EEUC [11], ACE [12], BCDCP [13], PEGASIS [14], TEEN [15], APTEEN [16], TTDD [17], CCS [18], HGMR [19], S-WEB [20], PEACH [21], MRPUC [22], MOCA [23], FLOC [24], Adaptive clustering [25], AWARE [26]) and the results are shown in Figure 1. The main reason that Voronoi [27] is the dominant structure adopted in existing clustering algorithms is that Voronoi structures are convenient for relevant data fusion and TPC. The sensors close to each other tend to have relevant data. The communication cost between those sensors can be also low. The sensors in a chain-based cluster have less relevant data since the chain may spread over a large area. Distributed control mechanisms provide a more flexible and robust service. For the reason that most existing work only concerns energy efficiency, numeric evaluation in MATLAB is mostly used. The remainder of this paper is organized as follow. Section II reviews the related existing work. The power consumption model adopted in this paper is introduced in Section III. In Section IV, we illustrate the motivation of our algorithm. Section V presents the detail implementation of BEE and the evaluation of BEE through simulation is shown in Section VI. We also provide the implementation for the multihop version of BEE—BEEM in Section VII. Section VIII discusses the problems in BEE(M) and the future work. Finally, the conclusions are drawn in Section-IX. II.

R ELATED W ORK

Due to its importance as a technique for improving energy efficiency, a wide body of clustering protocols and algorithms have been proposed and three well cited survey papers have been published [28][29][30]. LEACH [2] provides an elegant clustering routing approach that has inspired many varied solutions. After the CHs are randomly selected, they will broadcast their information to all the sensors in the network. Based on the received information, each sensor decides which CH it wants to join. Instead of using random CH election scheme, HEED [5] can select the sensors with high battery level to be CHs through the iteration CH election scheme. In the iteration CH election scheme, CHs are classified into two types: tentative and f inal CHs. Some initial CHs are selected randomly as tentative CHs. After each iteration, every sensor increases their probability to become a CH. Once the probability is over 1, the sensor will claim itself as a f inal CH. A tentative CH will give up to be a CH if it discovers a f inal CH in its communication range. The sensors

MATLAB

MATLAB

Compared With Direct MTE, Static LEACH HEED

are not covered by any f inal CHs will elect themselves to be CHs. This iteration CH election scheme guarantees that the probability of the phenomena that two sensors, within each other’s communication range, both become CHs is rare. Therefore it is can be deduced that the CHs are well distributed over the network and thus all the clusters have similar size. HEED involves significant overhead due to the heavy broadcast in each iteration. As the number of iterations required in the initial phase increases, the overhead and network delay are also increased. DWEHC [8] made an improvement on HEED by using sensors’ location information. It can achieve more balanced cluster size, and consequently achieve more balanced the power consumption on each sensor. However, location information of the sensors is not always available. In PEGASIS [14], every sensor in the network transmits its data to one of its neighbours. In this way, the gathered data is transferred from one node to another through a chain. A designated node (a node receives data from both sides) will send the assembled data back to the BS. PEGASIS is claimed as a distributed algorithm. However, every single node needs to obtain the global topology of the network. CCS [18] is a centralized clustering algorithm based on PEGASIS, which is a multiple chain based clustering algorithm. Considering the BS as the center, each sensor assigns itself a level number based on the signal strength received from the BS. For each level, the sensors perform transmission and fusion in the same way as in PAGASIS. A sensor that is elected as a CH will gather the data from all the other sensors on the same level and then transmit the fusion data to the CH in the next level that is closer to the BS. Once being assigned a level, a sensor will not change its level unless the BS’s location changes. This structure suffers from a problem that the sensors near the BS die soon from routing packets. Only total power consumption of the network is used to evaluation the algorithm. Whether the power usage through the network is balanced or not is concealed. S-WEB [20] is a spectrum structure based clustering algorithm. The first step in S-WEB is similar to CCS. All sensors are partitioned into layers based on their distance (measured but signal strength) to the BS. Then the BS does a 360-degree scanning sweep by sending out signal at one angel at a specific time. Sensors are clustered into cells based on the layer number and scanning angle. In each cluster cell, the sensor with the highest residual energy will be elected as the CH. All the sensors are responsible for forwarding packets. The cluster

IV.

TABLE II: Energy Dissipated Protocols

Transmission/Receiving (Eelect )

Transmit Ampilier (amp ) 2

LEACH

50nJ/bit

100pJ/bit/m

HEED

50nJ/bit

10pJ/bit/m2 (d < d0 ) 0.0013pJ/bit/m4 (d > d0 )

TABLE III: Simulation Parameters Type Network

Application

Parameters Network area Sink Number of Sensors Initial Energy Cluster radius Data packet size Broadcast packet size Data header size Round

Values From (0,0) to (100,100) At (50,175) 300 0.5 J 25 m 100 bytes 25 bytes 25 bytes 5 TDMA frames

structure of the network is fixed after performing S-WEB. It is not adaptive to the dynamic changes in the network, like node failure. The evaluation of S-WEB is only based on the comparison with a non-cluster routing—Direct Routing. In Table I, we summarize the properties of the 6 clustering algorithms. LEACH (11 out of 25 papers stated in Section I) and HEED (5 out of 25) are the two most referred clustering algorithms as benchmarks in the existing work. Few of the clustering algorithms consider network coverage. III.

P OWER C ONSUMPTION AND A LGORITHM P ERFORMANCE

LEACH claims that different assumptions about the radio characteristics will affect the performance of a protocol. Two most referred clustering algorithms, LEACH and HEED, adopted different models to compute energy consumption for long distance communication. As shown in Table II, in LEACH, the calculation of transmission power consumption is simplified as: ET x = Eelec ∗ k + amp ∗ k ∗ d2

(1)

where k is message length measured in bits and d is the distance from the transmitter to the receiver. In the further work, LEACH research team provides an advanced study on radio power consumption [3]. The calculation is specified as: ET x = Eelec ∗ k + amp ∗ k ∗ dn

(2)

2

When d < d0 , amp = 10pJ/bit/m and n = 2. When d > d0 , amp = 0.0013pJ/bit/m4 and n = 4. The value of d0 is a constant distance that is determined by the surrounding environment. HEED has adopted this power consumption model. Our research is also based on this model. The performance of a clustering algorithm is highly related to the parameter settings in the simulation. For example, if broadcast packet has the same size as data packet, heavy broadcast will significantly undermine the performance. Besides, node density also affects the impact of broadcast. We set our simulation parameters to be the same as in HEED, shown in Table III. 300 nodes are randomly deployed in a (0,0) ∼ (100,100) field with a BS located at (50,175).

M OTIVATION

Most existing clustering algorithms focus on maintaining the number of sensors that are still alive to extend the longevity, ignoring the distribution of the sensors. The coverage of a network is highly determined by the sensor distribution and it is crucial in most systems, like wildlife monitoring or battlefield sensing. To expose the network coverage problem in current work, three communication schemes are examined: direct routing, general LEACH and HEED. The experiment settings are the same as in HEED, shown in Table III. In HEED, each CH is set to use single hop to communicate with the BS. The number of nodes still alive after each round in the network is shown in Figure 2. LEACH and HEED performanced significantly better than direct transmission. However, the comparison between LEACH and HEED requires careful analysis. The first node died earlier in HEED than in LEACH. After the first node died in LEACH, all the sensors run out of power in a short period of time. Therefore, the last node died later in HEED than in LEACH. Depends on the definition for network lifetime (from the system starts till the first or the last node dies), LEACH and HEED can have different performances. However, in this paper, we aim to evaluate the network lifetime from another perspective. We argue that the number of nodes left in the network cannot present the Service of Quality (QoS) of a system. In Figure 2, around 450 round, we can see that LEACH and HEED almost have the same number of nodes in the network. The snapshots of the sensor distribution at 450 round for both protocols are shown in Figure 3. With the same number of sensors left in the network, we can see that LEACH has a better distribution as the sensors still alive can cover a slightly larger area than HEED. Depending on the emphasis of a system, the way to measure the lifetime of a network is not unique. When the first node or the last node dies is not the most important issue in term of network coverage. The coverage of the network should be considered when measuring the lifetime from the QoS perspective. Since different systems have different requirements, simply evaluating the network lifetime by the number of sensors is not convincing. In a system, we believe that some of the sensors in the network are more important than others on network coverage level. An extreme case is shown in Figure 4: area A has a higher node density than the rest of the sensing field. The nodes in area A have less impact on the coverage of the network than the nodes outside this area. The sensors that do not have a significant impact on the coverage of the network are allowed to die sooner than others. To implement multihop communication manner, the sensors can be partitioned into layers to adopt similar strategy in CCS or S-WEB. V.

T HE BEE P ROTOCOL

In this section, we introduce BEE protocol. We deliver the network assumptions first and then the detail implementations. A. Network Assumptions In this paper, several assumptions are applied to the network, most of which are the same as in HEED.

However, we do not make any assumptions on: 1) network distribution, 2) node location awareness, 3) node synchronization, 4) global topological information or 5) the relation between sensing radius and communication radius (normally researchers assume that sensing radius is longer than communication radius to avoid the coverage problem). B. Improved Iteration CH Election In HEED, the initial probability that a sensor elects itself to be a CH is Eresidual CHprob = Cprob × (3) Emax Fig. 2: Number of sensors still alive in the network.

(a) LEACH

(b) HEED

Fig. 3: Distribution of nodes still alive after 450 rounds.

•

The connections between sensors are symmetric, which means two nodes can communicate with each other using the same transmission power.

•

Nodes are randomly deployed in the network. Some areas may have a higher node density than other areas.

•

All the sensors and the BS are placed at fixed locations. The sensors in the field are powered by build-in batteries that cannot be recharged.

•

All the nodes are homogeneous and have similar communication and computation capabilities.

Cprob is the initial CH probability (Both LEACH and HEED set it to be 5%). If a sensor is not covered by any CHs, it will elect itself as a tentative CH if a random generated number is smaller than the value of CHprob . After each iteration, CHprob is increased twice (maximal value is 1). Once CHprob reaches 1, a tentative sensor will declare itself as a f inal CH. If a sensor is not covered by any f inal CHs, it will declare itself as a f inal CH when its CHprob = 1. A sensor will terminate the iteration process when its CHprob = 1. To void really small value for CHprob , it is set to the max value between Cprob × Eresidual and Pmin = 10−4 . Otherwise the number of Emax iterations can be unnecessarily large. Since Cprob starts from 5%, a high energy sensor still needs at least 6 iterations to have a chance to declare itself as a f inal CH (0.05 × 2Ntier −1 can be bigger than 1 only when Niter ≥ 6). As Eresidual of a sensor decreases, it needs more iterations to terminate the CH election process. To address the issues highlighted in Section IV, two improvements are made in the CH election process in BEE. 1)

2)

Number of iterations: The number of iterations to terminate the CH election process has a significant impact on the network latency and congestion. Therefore reducing the number can reduce the overhead of the iteration CH election process. Node density: Sensors in a high-density area are allowed to die sooner than the sensors in a low-density area for the purpose of maintaining the coverage of the network. In BEE, we believe that if a sensor’s node degree is high, it is reasonable to assume that the density around this sensor is high. The node degree of a sensor is referred as the number of sensors in its communication range.

Based on HEED, in BEE, considering local density, CHprob should be calculated as:   Eresidual N ode Degree CHprob = Cprob × ×min , 1 (4) Emax Davg

Fig. 4: Non-uniform distributed WSN.

where Davg is the average density of the network and it is calculated as: N umsensors Davg = πR2 × (5) Area R is the default communication range of the sensors (normally it is set to the cluster radius), N umsensors is the total number of sensors in the network and Area refers the area of the sensing field. Davg is also the value for average node degree.

TABLE IV: CH Self-election Table C1

C2

C3

CH Status

1

1

1

Final

0

1

1

Final

1

0

1

Final

1

1

0

Final

1

0

0

Tentative

To reduce the number of iterations, we separate the factors and in Formula  (4) into three parts: Cprob , Cen = Eresidual Emax  N ode Degree Cde = min , 1 . Three conditions that are used Davg to determine whether a sensors can elect itself as a f inal or tentative CH are: 1) 2) 3)

comparing with LEACH and HEED. Table III lists the simulation settings for the experiment parameters, which are the same as in HEED. The power consumption model used to evaluate BEE is also the same as in HEED, shown in Table II. A. Network Distribution Figure 5 shows after 450 rounds performing BEE, the snapshot for the distribution of the sensors still left in the network. Comparing with the distributions shown in Figure 3 for LEACH and HEED, BEE can provide better coverage at 450 round, with the same number of nodes as LEACH and less number of nodes compared with HEED.

C1= hRandom (0, 1)E≤ Cprob i D C2 = Eresidual ≥1 D Emax E C3 = N odeDDegree ≥ 1 avg

As in HEED, Cprob is set to be the optimal CH ratio—5%. After each iteration, the value of Cen and Cde are doubled respectively. A sensor will terminate its own CH election thread when either Cen or Cde reaches 1. By separating the factors, we aim to decrease the number of iterations CH election process to construct the CH set. The status of the CH depends on which conditions are true as shown in Table IV. If two of the three conditions are true, the sensor will elect itself to be a f inal CH. If a sensor cannot communicate with any sensors, it will elect itself to be a CH directly without executing the iteration CH election process. C. Algorithm Analysis In BEE, each sensor has the same probability to become a tentative CH. The probability C1 remains the same after each iteration. C2 and C3 are increased after each iteration. In HEED, since the probability to become a tentative or f inal CH depends on CHprob and this value is doubled after each iteration, more sensors tend to become tentative CHs. The total number of broadcast messages in the network is the sum of the number of sensors who ever claim to be tentative CHs and the number of sensors who ever claim as f inal CHs. Since a tentative CH will give up being a CH when it discovers a lower cost CH in its communication range, tentative CH generation cannot help the process determine quicker. Meanwhile it increases the number of broadcast activities. Therefore the probability to become a tentative CH should not be increased. Decomposing the probability for a sensor to become a CH into three parts can elect CHs from three different perspectives: randomly, residual energy and node density. If a node has a higher degree than the average, it always will elect itself as a f inal CH and will die quickly, which supports our expectation that the sensors in a high-density area are allowed to die sooner than sensors in a low-density area. VI.

P ERFORMANCE E VALUATION

The general comparison between BEE(M) and other clustering algorithms is shown in Table I. In this section, the performance of BEE will be examined through simulating,

Fig. 5: Sensor distribution after 450 rounds using BEE.

B. CH rate Comparing the CH percentage in Figure 6a, we can see that BEE has similar number of CHs as HEED. In HEED, the CH percentage increases to 1 at the end. This is because all the sensors still alive are no longer in each other’s cluster range and then every sensor is required to be CH to transmit data directly to the BS. It has been proved that in HEED the elected CHs are well distributed in the network and can cover the whole sensing area. The case that two CHs in each other’s cluster range is rare. Since BEE does not need more CHs than HEED, the CHs elected through improved iteration CH election process in BEE can also cover the whole sensing area. C. Clustering Iterations The number of iterations in the clustering forming phase determines the overhead of the algorithm. Reducing the number of required iterations in each round can reduce 1) the clustering time delay and 2) the number of broadcast packets. The comparison of the number of iterations in each round is shown in Figure 6b. By separating CHprob into three parts, the number of iterations in each round is significantly reduced in BEE. At the end, for HEED, the number of iterations suddenly drops to 0 because no sensor is still alive in the network. The number of iterations of HEED can increase from 6 to 15. When the battery level is high, as we mentioned in Section V-B, 6 iterations are necessary since Cprob = 5%. When the battery level is low, it takes 15 iterations as Pmin = 10−4 . However, the number of iterations for BEE will not increase significantly as the sensor batter level decreases.

(a) CH percentage.

(b) The iterations required in each round.

(c) Number of sensors still alive.

Fig. 6: Comparison between HEED and BEE

D. Longevity The number of sensors still alive sensors in the network is shown in Figure 6c. In the period from 0 till 450 round, more sensors died in BEE than in HEED and LEACH. After 600 round, BEE had more sensors left in the network. In long term, BEE has longer network lifetime than HEED and LEACH. In the next section, we will prove that the sensors died at the beginning have little impact on the coverage of the network. E. Network coverage The cluster radius in both BEE and HEED is set to be 25m. The sensing radius is set to be 10m. To simplify our problem, we partition the network area into grids of the size 10m × 10m rather than circles. Through this way, the sensing field is partitioned into 100 cells. In each cell, if there is a sensor still alive, we assume this area can be monitored by system. To guarantee the network coverage, a clustering algorithm should be able to cover the cells maximally. Since the sensors are randomly deployed in the network, the initial coverage with 300 sensors is 93 cells, as shown in Figure 7. The coverage of the network after each round is shown in Figure 8.

Fig. 7: Sensing grid of the network at the initial state.

We can see from Figure 6c that nodes started to die around 100 round for BEE. However, in Figure 8, BEE starts to loose coverage around 180 round, which means the sensors start to die from 100 round till 180 round do not have any effect on the coverage of the network. For long term, BEE can provide better coverage than HEED and LEACH. VII.

M ULTIHOP I NTER - CLUSTERING BEE–BEEM

The communication between the CHs and the BS is called inter-cluster communication. All the experimental results in this paper are drawn from a 100m × 100m network. When the network size scales, the sensors that are far away from the BS may die much earlier than the sensors close to the BS by using direct inter-cluster transmission. If the sensors do not support long distance communication, the connectivity of the network is hard to guarantee. For the above reasons, it is necessary to support multihop inter-cluster communication. 60% of the 25 clustering algorithms mentioned in Section I support mutlihop inter-cluster communication. Besides, multihop inter-cluster routing can further even the power usage on each individual sensor through the network.

Fig. 8: Network coverage.

HEED declared that many multihop communication protocols could be used to guarantee a connected inter-cluster overlay graph. It provided a proof on a uniformly distributed network. However, it failed to provide the detail implementation. Here we propose a multihop communication approach special for WSN. In BEEM, we adopt the same idea that is used in CCS and S-WEB in order to organize the sensors into layers as shown in Figure 4. The higher-layer CHs transmit data to the

1-lower layer CHs. The BS will broadcast a beacon signal to all the sensors in the network at the initial stage. Based on the received single strength, the distance between a sensor and the BS can be estimated from the Log Distance Path Loss Model. Based on the distance between a sensors and the BS, every sensor assigns itself a layer index. Supposedly the cluster range is T r, and then the maximum value for the distance from a CH to its nearest CH will be 2T r. The radius difference of two adjoining layers should be 2T r. If a CH wants to transfer data back to the BS, it will transfer the data to one of the lower layer CHs first. The CH transmission range should be at least 2T r to guarantee it can communicate with its nearest CH. If R = 2T r, the CHs at layer n can transfer data to n − 1 layer. If R = m × 2T r, the CHs at layer n can transfer data to n − m layer. In BEEM, we set R = 2T r. The experimental results are shown in Figure 9. The energy cost of forwarding packets is set to be 10pJ/bit/m2 . BEEM can provide better network coverage and longer overall lifetime.

tradeoff between the benefit and the energy/time cost requires careful analysis. B. Various Combinations of CH Election Conditions

Fig. 10: Comparing between C2 || C3 and C2 && C3 As we presented in Section V, BEE used C2 or C3 (C2 || C3) as the condition for a sensor elected itself as a f inal CH. Instead of using C2 || C3, using C2=1 and C3=1 (C2 && C3), the iteration will change from 3 to 15 in the period of 1000 rounds. For C2 && C3 case, it improves the coverage performance between 0 and 450 round, compared with C2 || C3 case, shown in Figured 10. However, it loses more coverage from 450 till 100 round. For both cases, in general, the coverage is better than HEED. Fig. 9: Coverage comparison between BEE and BEEM

VIII.

D ISCUSSION

In this section, we will discuss the usability of BEE(M) and future work. A. Local density As we can see from Figure 8, from 200 round to 400 round, the network coverage of BEE is slightly lower than HEED. The major reason is that some of the dead sensors are essential. The sensors were elected as f inal CHs for their high density (not for high energy since they die earlier and they should have low energy level). Ideally, if the sensors are well distributed in the network with 100 cells, the coverage of the system should not be undermined when the total number of sensors still alive is more than 100. In a 100m × 100m network, the high degree sensors are normally the sensors located in the center of the network. As the size of the network increases, node degree will have a better correlation with the local density. Therefore, when the network size is not large enough, node degree can hardly reflect local density and another scheme should be used to estimate the local density. However, since BEE(M) is a distributed algorithm, we do not tend to use global information centrally or assume each sensor has global topological map. To deliver a more accurate value for the local density, information exchanging between a sensor and its neighbors is necessary. A

In BEE(M), local density and residual power are used as CH election conditions. Other metrics can also be used and should be considered in future work, for example, distance/hops to the BS or node ability. Base on different objectives of the clustering algorithms, the choice for CH election metrics is also different. C. Cluster Range The cluster range can affect the performance of a cluster algorithm. In order to compare with HEED, we set its value to be the same as in HEED. However, its optimal value depends on the area of the sensing field and the hardware implementation details. Besides, the cluster range should be able to adapt the density of the network. D. Initial Cluster Header Rate LEACH concludes that 5% CH rate shows the best performance of the algorithm. HEED also used this value as the initial CH rate. In LEACH, the 5% CH rate for a network is calculated from the cluster range. Since the cluster range is 25m, in a 50*50 m2 area, there should be at least 5 CHs. The total number of sensors is 100. Then the CH ratio is 5%. If the cluster range, node density or total number of sensors changes, the optimal CH ratio may also change. As we mentioned in Section VIII-C, the value of cluster range should be adaptive to node density. Since the cluster range and the node density affect the CH ratio, the relation between CH ratio and cluster range and how they should change as the network distribution changes requires further analysis.

IX.

C ONCLUSIONS

In this paper, we propose a new perspective to measure the lifetime of a WSN: the sensing coverage of the network has more meaning than the number of sensors that are still alive in term of QoS. Therefore we claim that the longevity of a network should not be evaluated only based on the time that the first node dies or the last node dies, but also the network converge. To guarantee the coverage of the network, in this paper, we provide a novel clustering algorithm— Balanced Energy Efficiency (BEE) clustering algorithm and its Multihop version (BEEM)—that exceed HEED and LEACH in two ways: 1) System operating time: time from the system starts till the last node dies. 2) System operating quality: the sensing coverage maintaining ability. Multihop communication supported version BEEM can be used in a larger network to even the power usage through the network. Future work involves the studies on local density estimation, the impact of cluster range and cluster header rate. R EFERENCES [1]

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