Coverage of communication-based sensor nodes deployed location

Journal of Systems Engineering and Electronics Vol. 21, No. 4, August 2010, pp.698–704 Available online at www.jseepub.com

Coverage of communication-based sensor nodes deployed location and energy efficient clustering algorithm in WSN Xiang Gao1, * , Yintang Yang1 , and Duan Zhou2 1. College of Microelectronics, Xidian University, Xi’an 710071, P. R. China; 2. College of Computer Science and Technology, Xidian University, Xi’an 710071, P. R. China

Abstract: An effective algorithm based on signal coverage of effective communication and local energy-consumption saving strategy is proposed for the application in wireless sensor networks. This algorithm consists of two sub-algorithms. One is the multi-hop partition subspaces clustering algorithm for ensuring local energybalanced consumption ascribed to the deployment from another algorithm of distributed locating deployment based on efficient communication coverage probability (DLD-ECCP). DLD-ECCP makes use of the characteristics of Markov chain and probabilistic optimization to obtain the optimum topology and number of sensor nodes. Through simulation, the relative data demonstrate the advantages of the proposed approaches on saving hardware resources and energy consumption of networks.

Keywords: wireless sensor network, probability distribution function, Markov chain, received signal strength indicator, Gaussian distribution. DOI: 10.3969/j.issn.1004-4132.2010.04.025

1. Introduction Wireless sensor networks (WSN) adopt low-power and adaptive self-configuring communication protocols, which restrict networks resources usage [1] and require optimum deployment of sensor nodes to achieve effective energy consumption and signal communication [2]. Hence, when assuring the deployed precision, how to efficiently configure sensor nodes to attain effective coverage of signal communication and make use of deployment of these nodes to get energy efficient consumption have been the critical issues. For WSN, energy consumption is one of the main research fields. Reference [3] proposed a low-energy adaptive cluster hierarchy (LEACH) algorithm. The idea of clustering and selecting cluster heads (CHs) in turn in Manuscript received August 31, 2009. *Corresponding author. This work was supported by the Major State Basic Research Program of China (B1420080204), National Science Fund for Distinguished Young Scholars (60725415), and the National Natural Science Foundation of China (60606006).

terms of random probability are introduced in LEACH, and then many other clustering algorithms have been proposed [4–6]. These algorithms make energy consumption balance among sensor nodes but consider sensor nodes can directly communicate each other in WSN. However, signal intensity decreases with communication distance and electromagnetic interference (EMI) is able to influence effective signal transmission in practical scenarios [7], the multi-hop communication strategy is proposed to reduce the energy consumption. The methods of cardinalities and multi-hop communication in each cluster are used to keep the loads of CHs close to their average load in inter-cluster load balance [8], which lead to lower energy consumption and longer lifetime of the networks than that in one-hop communication strategy. In above mentioned algorithms, the assumption is that sensor nodes are deployed randomly in sensitive areas. One of the disadvantages of random deployment is easy to expend large number of hardware resources, so it is better to take account of introducing a nonrandom locating deployed algorithm to assure effective communication coverage connectivity in each deployed area and save hardware resources. Hence, deterministic deployments based on optimal patterns are more likely in missions when sensitive areas are physically accessible [9], and these patterns of nodes deployment may be uniform, Gaussian or Poisson distribution, such as uniform distribution in [10– 12]. However, current researches on sensor nodes deployment mainly focus on ensuring sensing areas connectivity through optimizing sensing coverage probability (CP). For example, [13] devised the nodes deployed model based on Gaussian distribution and concluded that sensing CP was improved with the increase of standard deviation of the deployed errors; [12] introduced missing probability to obtain optimal number of deployed sensor nodes and deployment according to the terrain model and the deployed precision, and reformed the algorithm proposed in [14], which optimized CP to improve deployed efficiency in terms of

Xiang Gao.: Coverage of communication-based sensor nodes deployed location and energy efficient...

uncertainty of sensing probability. Thus, considering effective signal communication coverage in the whole deployed field and energy efficient consumption in this paper, two sub-algorithms are proposed. One is distributed locating deployment based on the efficient communication coverage probability (DLDECCP) algorithm borrowing ideas of [12–14]. The other is the multi-hop partition subspaces clustering (MPSC) algorithm, where the optimal number of CHs is computed according to sensor nodes’ deployment from DLD-ECCP, based on [8]. Finally, simulation results show that energy consumption and hardware resources are saved maximumly in WSN, when assuring the deployed precision and finishing effective communication coverage.

2. Mathematical model of the state spatial partition 2.1 Probability distribution of signal transmission In WSN, all nodes can be deployed in the partitioned grid areas through special equipments [15] in terms of certain deployed precision. However, the signal strength of a received radio among senor nodes is acquired through a received signal strength indicator (RSSI). Hence, CP on effective signal communication coverage of each partitioned grid area is able to be calculated through the probability distribution function (PDF) of RSSI. As known, average RSSI fades exponentially with the nth power of the distance from the transmitter to the receiver [16], then the signal envelope of RSSI obeys Rayleigh distribution and the normalized PDF of current testing RSSI decreases exponentially with negative reciprocal of average RSSI [17]. So it could be deduced that the normalized PDF of current testing RSSI is equivalent to vary exponentially with the n-th power of the distance from the transmitter to the receiver. The function of average RSSI is given as follows [17] RSSI = −(10n lg d + A) (1) where A is the measured signal power at a certain distance, usually one meter. When RF-level is set to 20 dBm according to real configuration, A maintains about 40 dBm. d denotes the distance between transmitter and receiver. The chip of CC2431 from TI is chosen as testing hardware of RSSI and the tested parameters are received and shown by the console connecting with the base station (BS) in this paper. Eight receiver nodes are deployed in rectangle area orderly and all the distances between neighbor nodes are four meters. The transmitter node locates at the center of the area. Testing results show that (1) is able to be better modeled when n ranges from 2.75 to 3.25. The mean value of n, which is three, is used in this paper. Therefore the normalized PDF of current testing RSSI is obtained,

699

which is the receiver node’s signal power at point (a, b) from transmitter node at point (x, y) pab (x, y) = exp [−αd3ab (x, y)]

(2)

α is a constant and has connection with nodes’ physical characteristics and EMI in practical scenarios. 2.2 Transition probability of state spatial partition DLD-ECCP is a distributed algorithm and the locations of deployed nodes have uncertainties, so a single-step deployment scheme is more suitable. Based on the above factors, state spatial partition of the deployment is a discrete and stochastic process and the current deployed node is decided by communication CP of each grid area which is calculated by the nodes of previous deploying steps. Therefore, state spatial partition possesses the characteristics of Markov chain (MC). However, taking into account the errors of the deployment, gaussian distribution is modeled as the joint probability density function of the errors [13], which is expressed as     (y  − y)2 (x − x)2 − exp − exp − 2σx2 2σy2   ϕxy (x , y ) = 2πσx σy (3) The point at (x , y  ) denotes the actual position of the deployed node during single-step deployment and the grid at (x, y) is the target position of the deployed node in (3). The variances of σx and σy are assumed independent and identically distributed conditioned at X and Y dimensions respectively in terms of the results of randomized trials. Because it is difficult for computing CP of each grid area directly, the problem is how to guarantee effective communication CP being able to be converted to calculate a lost coverage probability (LCP) indirectly. In this case, the LCP function of the node at grid (a, b) from the node at grid (x, y) could be defined as ζ¯ab (x, y) = 1 − pab (x, y)

(4)

where pab (x, y) denotes CP estimation of the conditional probability for a grid (a, b) which is covered by effective signal from a sensor that is supposed to be deployed at (x, y). Then the function is given by  pab (x , y  )ϕxy (x , y  ) p ab (x, y) =

(x ,y  )∈Sur(x,y)



ϕxy (x , y  )

(5)

(x y  )∈Sur(x,y)

where Sur(x, y) denotes the total area surrounding all possible sensor locations.

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DLD-ECCP is similar to the likelihood estimation in statistics, so the transition probability of state spatial partition from the state i to the state j through k + 1 steps transition is able to be obtained by Chapman-Kolmogorov equation. So the function could be written as follows  (k) (k+1) (1) pij (t) = pil (t)plj (t + k) =

(k+1)

pij





{l|(a,b)∈Grids}

{1 −

ζ¯ab {xk , y k |(xk , y k ) ∈ i}·

k=1

pab [x∗ , y ∗ |(x∗ , y ∗ )

∈ j]}

(6)

ST denotes the state spatial set of deployment, and (x∗ , y ∗ ) denotes the new introduced state of deployment which is excluded from ST in (6). Let (a, b) traverse all the spatial grids, so the state l is ergodic. At the same time, we de(k+1) fine the transition probability of pii (t) is equal to zero.

(8)

S(j|(x∗ ,y∗ )) = arg min P 1 (t) = arg min(pij (t)) i = j;

(9)

t = 2, . . . , n

Through (9), the optimal deployed grid is obtained at the point (x∗ , y ∗ ). The whole process is iterative until S is less than the given threshold STH . Finally, through this method, the optimal topology containing minimum number of deployed nodes is able to be obtained. To summarize, DLD-ECCP according to MIN-DEP is achieved as follows: 1.

While S(j|(x∗ ,y∗ )) < STH and (x∗ , y ∗ ) ∈ CO

3. Implementation of two sub-algorithms After finishing nodes deployment, the MPSC algorithm is introduced which divides a sensor field into several regular subspaces to ensure average energy consumption in each subspace, according to the regular nodes deployment acquired from the simulation of DLD-ECCP.

i = j; t = 2, . . . , n

Thus, the optimal position of the deployed node is obtained in every step through MIN-DEP from

l length(ST )

(t − k),

2.

for x∗ = 1 to m and y ∗ = 1 to m

3.

/ ST if (x∗ , y ∗ ) ∈

4.

t = t + 1; t = 2 : n;

5.

sample 1 000 times, calculate pab (x∗ , y ∗ ) and (8);

3.1 Estimation of DLD-ECCP

6.

case (type = MIN − DEP) do (9);

The DLD-ECCP algorithm is proposed based on the assumption that CP of each grid area is able to achieve the threshold, which is the probability that could ensure the efficient communication coverage, and then a minimum deployment scheme (MIN-DEP) is drawn from DLD-ECCP to obtain the minimum number of deployed nodes. The sensor field is partitioned into m × m equidistant twodimensional spatial grid areas, and BS is deployed at the central grid as the referenced origin. All the deployed nodes are configured omnidirectional antennas to receive and transmit data from different nodes. Through the initialization, the sets of CO and ST , which store undeployed grid areas and deployed nodes as well as their locations respectively, are obtained. After fulfilling the initialization, the single-step deployment is executed in terms of the one-step transition probability matrix P 1 (t) obtained from (6), and the diagonal vectors are zero. This matrix can be rewritten as follows ⎞ ⎛ 0 p12 (t) · · · p1m (t) ⎜ p21 (t) 0 · · · p2m (t) ⎟ ⎟ ⎜ P 1 (t) = ⎜ (7) ⎟ .. .. .. ⎠ ⎝ . . .

7.

k = k + 1;

8.

add (x∗ , y ∗ ) to ST and delete (x∗ , y ∗ ) from CO;

9.

End

pm1 (t)

···

···

0

where (k) pij (t) = pil (t − k)ζ¯lb (x∗ , y ∗ |(x∗ , y ∗ ) ∈ j) =

10. End Optimal topology, obtained through DLD-ECCP, saves the hardware expense extremely. The computational complexity for MIN-DEP is O(m2 ). The probability of average communication coverage is introduced to estimate our algorithm, which is defined as 1− Covavg =



 (a,b)∈Grid



sxy

(x,y)∈ST

m×m

(10)

3.2 Load-balanced and optimal routing of MPSC It is known that the number of deployed nodes is an approximate average in unit deployed area according to the deployment from DLD-ECCP. Therefore this research background based on uniform distribution accords with the conclusions from [10–12]. MPSC is proposed based on the distribution of deployed nodes from DLD-ECCP and grid-based cluster partition method [18], where dividing deployment area into the appropriate number of subspaces

Xiang Gao.: Coverage of communication-based sensor nodes deployed location and energy efficient...

with the same size ensures that the number of sensor nodes in each subspace is approximately equal and keeps the loads of each subspace close to their average load and the better performance of the lifetime of networks concluded from [8]. Considering the influence of EMI and the effective radio radius, the MPSC adopts a multi-hop strategy between member sensor nodes and their corresponding CH and between CHs and BS. So it becomes important to search optimal paths. • It is assumed that all sensor nodes have the same radio radius and optimal paths are obtained by creating the process of minimum structure trees which is similar to the hierarchical based algorithm [19]. Making use of hierarchical idea, source node broadcasts advertisement packet (ADV) including its ID and location to the sensor nodes within its radio radius. After receiving and reading ADV, sensor nodes create an individual information list including their ID, hops which are added one and the distance between source node and itself, then relay ADV attaching their information lists to sensor nodes located at the lower layer nodes (LLNs). When each LLN receives ADVs from different upper layer nodes (ULNs) each time, it aggregates the distance of each hop from ULNs and adds one to the hops in individual information list respectively. The process is performed circularly till all sensor nodes receive ADVs. The broadcasting process is separated into several frames according to the ratio of the farthest distance from BS to marginal area and the radio radius. Because one sensor node may receive several ADVs from different ULNs, every information list stores ULNs data in ascending hops sort order firstly and then by the sum of the distance of each hop from source node to different ULNs. • CH is selected in each partitioned subspace. The commands of partitioning subspaces are executed in BS and the information of partitioning subspaces is broadcasted to all sensor nodes through ADV in terms of the hierarchical based algorithm [19]. Each node receives ADV, and then joins into individual subspace according to the central distance algorithm of the subspaces. The initial phase of creating clusters is called setup phase which is executed as follows: Step 1 Each node receives the information about the size and central position of each subspace in ADV from BS according to the hierarchical based algorithm. Step 2 Each node chooses the subspace whose central position is the nearest to node’s position as an individual initial cluster. Step 3 Each node in cluster draws individual waiting time in proportion to its distance from the central position of the cluster, such as one-fourth distance. Step 4 When the waiting time arrives, each node

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judges whether it has received a hello packet which is sent as ADV in the corresponding cluster. If not, this node is chosen as CH of this cluster and then creates a hello packet and broadcasts the packet; otherwise, this node becomes the member node and relays the hello packet. This CH will be the most close to the central position of the cluster. • Another phase is transmission phase. All the member nodes in the cluster and CHs in networks search their optimal paths according to the minimum structure trees and transmit their data to BS according to an inverse optimal path stored in nodes’ information lists. This process is defined as a round, and each current CH selects the most energetic node from its member nodes as the next-round CH. Non-CHs join into an individual cluster according to Voronoi diagram next round. All data from member nodes are compressed in corresponding CHs and transmitted to BS by CHs. It is assumed that this node is dead when its left energy is less than a given threshold. The information list of each node is searched in order until all ULNs are dead. Namely, this branch path is blocked and then cut off. Even though the optimal energy consumption in the whole networks is not able to be computed quantificationally, the deployed density of CHs could be used to obtain approximate optimal energy consumption [20]. An assumption is made that the free space model [3] is applied to MPSC. The functions [3] of energy dissipation of the transmitter and receiver respectively are expressed as ET X = K · Eelec + K · εf s · d2

(11)

ERX = K · Eelec

(12)

Eelec denotes the energy per bit that is necessary for digital processing, modulation, and εf s denotes the energy per bit dissipated in the amplifier for the free space distance d transmission. K denotes that K-bit packet is sent. The variables λ0 and λ1 denote the deployed densities of member nodes and CHs respectively. According to the characteristics of Voronoi diagram [21], if h is the random variable denoting the sum of the hops among sensor nodes in the corresponding cluster and let r denote the radio radius of the sensor node, the expectation of h could be deduced by  2πλ0 +∞ 2 x exp{−λ1 πx2 }dx = E(h) = r 0 λ0 3/2 2λ1

·r

(13)

where dBS is the distance from CH to BS. It is assumed that BS is located at the center of the square area of side 2a, where A = 2a × 2a. Then, in [20] E(dBS ) ≈ 0.765a

(14)

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Define d2CH as the sum of the square distance of one hop among all the sensor nodes in each cluster. Then E(d2CH ) = r ·

λ0

(15)

3/2

2λ1

Define EM , ECH and Ecluster as the expectations of energy consumption of the whole member nodes in each cluster, one CH and entire one cluster respectively. EDS represents the energy per bit for digital processing. Then

2K · Eelec ·

3/2

2λ1

ECH = K · EDS ·

·r

+ K · εf s · r ·

λ0 3/2

(16)

λ0 + K · εf s · E(dBS ) · r + λ1

λ0 E(dBS ) · Eelec = K · EDS · + r λ1 0.765a · Eelec K · εf s · 0.765a · r + 2K (17) r The variable Etotal denotes the expectant sum of total networks’ energy consumption that is able to deduced by Etotal = A · λ1 · EEcluster = A · λ1 · (ECH + EM ) (18) We substitute (16) and (17) for (18) and Etotal is minimized by setting the derivative of Etotal with the corresponding value of λ1 to zero. Then  2 3 1/2 1/3  q p q λ1(opt) = − + + + 2 2 3 −

q − 2



q 2 ) + 2

where p=−

3 1/2 1/3 p 3

B4 2λB 2 − A2 3A4

2B 6 2λB 2 λ2 B 2 − − 27A6 3A2 A2

(20)

These parameters in (20) are given as follows A = 2Eelec · E(dBS )/r + εf s · r · E(dBS ) − EDS B = Eelec/2r + εf s · r/4

4. Simulations of nodes’ deployment and energy consumption of WSN

2λ1

2K



q=−

and the number of sensor nodes of the networks n = Aλ.

EM = 2K · Eelec · E(h) + K · εf s · E(d2CH ) = λ0

and

(19)

We consider a scenario where the examined networks consist of m × m = 31 × 31 grid areas in the sensor field with dimensions 240 m×240 m. The sensing range of each sensor is 4 m, so each grid is 8 m far away from each other. According to the empirical conclusion, the attenuation parameter and effective radio radius are set to α = 10−4 and r = 50 m respectively. Figure 1 compares the number of deployed nodes in two different schemes in DLD-ECCP which are MIN-DEP in Fig. 1(a) and random deployment scheme (RAN-DEP) in Fig. 1(b). From the simulations, the number of deployed nodes is increasing with the decrease of STH and the increase of the variances of σx and σy respectively, namely with the increase of CP and the deployed errors of the nodes respectively. The scheme of selecting optimal places of MIN-DEP saves about 2.5 times hardware resources as small as RAN-DEP. Fig. 2 shows that RAN-DEP attains higher Covavg than MIN-DEP because more nodes are deployed in the field in RAN-DEP. However, MIN-DEP in DLD-ECCP is chosen as an appropriate deployment scheme based on the precondition of the certain Covavg and deployment cost.

Fig. 1 Number of deployed nodes for different schemes with different variances and thresholds

Xiang Gao.: Coverage of communication-based sensor nodes deployed location and energy efficient...

703

According to (19), we conclude that λ1(opt) ≈ 0.243 8× 10 , and the optimal number of subspaces partition is Z = λ1(opt) × A = 14.042 9. So Z is equal to 16 according to the results in [18] where the absolute difference value between Z and the number of optimal clusters is not able to exceed 2. The results from Fig. 4 prove the correctness between the simulation and computation. −3

Fig. 2 Average CP Covavg with two deployment schemes when σx = σy = 1

According to MIN-DEP in DLD-ECCP, the number of deployed nodes is 67 except BS and the networks connectivity is round 7 when σx = σy = 1 and STH = 0.7. For our experiments of MPSC, these parameters [3] in (19) are given as follows: a = 120, EDS = 5 nJ/bit/signal, K = 4 000 bit, Eelec = 50 (nJ/bit), εf s = 10 (pJ/bit/m)2 . The topology of nodes and Voronoi diagram partition are displayed in Fig. 3(a). Optimal transmitting paths among nodes in the cluster and between CHs and BS are shown in Fig. 3(b), where ray real lines denote the paths of interclusters and black broken lines denote the paths in clusters based on creating minimum structure trees in MPSC.

Fig. 3 The topology about sub-paces and optimal paths partition

Fig. 4 Average energy consumption for different number of partition subspaces (n = 67, r = 50 m)

It is seen that MPSC has better performances of lifetime and energy effective consumption compared with other algorithms which are LEACH-C [3] and multi-hop minimum trees (MHMT) without clustering described in Section 3.2 in Fig. 5. It is convenient for simulation that initial energy of each sensor is set to 0.3 J. The curve of MPSC in Fig. 5(a) indicates that energy attenuation is average, so MPSC proves the inter-cluster load balance and average energy consumption each cluster. Even though MPSC has the longer life time than other algorithms given in this paper, the slope value of curve is maximum when the number of dead nodes is more than 20 in Fig. 5(b). Because LLNs are not able to find the transmitting paths, ULNs compel the death of LLNs.

Fig. 5 Life-time and energy consumption between different algorithms

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5. Conclusion In this paper, optimization problems about sensor networks configuration and energy consumption are formulated in the context of network topology and communication protocol, where the deployed strategy of optimal networks resources is attained to provide sufficient communication coverage and the energy efficient routing protocol is applied in this networks topology to obtain the minimum energy consumption respectively. DLD-ECCP and MPSC solve these problems well in this paper and present high performance.

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Biographies Xiang Gao was born in 1982. He received B.S. degree from Nanjing Normal University in 2004. He is now a Ph.D. candidate in College of Microelectronics, Xidian University. His current research interests include wireless sensor networks, target location and network on chip system. E-mail:[email protected] Yintang Yang was born in 1963. He is a professor in College of Microelectronics, Xidian University. His research interests mainly include wireless sensor networks, VLSI design and SOC system. E-mail: [email protected]

Duan Zhou was born in 1957. She is a professor in College of Computer Science and Technology, Xidian University. Her research interests mainly include wireless sensor networks, SOC system and embedded systems. E-mail: [email protected]