A Localization Scheme of Wireless Sensor Networks Based on Small

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1 A Localization Scheme of Wireless Sensor Networks Based on Small World Effects Nan Jiang, 2 Xiao xiang, 3 Chen Huan * East China Jiao Tong University, jiangnan8@gmail.com 2 East China Jiao Tong University, 2xiaoxiang@gmail.com 3 East China Jiao Tong University, chenhuan2@gmail.com Abstract Small-world networks have attracted considerable interest over the past few years. Their universal characteristics, including small average path length and large clustering coefficient, have make smallworld effects to be applied in wireless sensor network (WSN) more and more widely. Aiming at localization deficiency of these large networks, an improved localization scheme (SWLS) based on multidimensional scaling (MDS) is designed and applied to wireless sensor networks with small-world effects. By adding a few reliable links, SWLS can not only reduce average energy consumption and average path length but also balance energy consumption. Furthermore, the proposed algorithm can achieve comparable localization performance. Keywords: Small World Effects, WSN, MDS, Clustering Coefficient, Average Path Length, Shortcuts. Introduction The advances in the wireless communications and MEMS based sensor technology have enabled the development of relatively inexpensive and low-power WSN [-3]. Large-scale WSN with hundreds and even thousands of very small, battery-powered and wirelessly connected sensor and actuator nodes are becoming a reality. However, there are several challenges that arise in the design of such large and autonomous sensor networks. Distinguished from traditional wireless networks, WSN is characterized of severe power, computation, communication bandwidth, and memory constraints. Therefore, one of the main challenges is to make them as energy efficient as possible. In other words, due to the strict energy constraint, energy resource of WSN should be managed wisely to extend the lifetime of sensors. Aiming at the task allocation in multi-target tracking of wireless sensor networks, the discrete particle swarm optimization based on nearest-neighbor is presented to reduce the communication energy consumption between nodes [4]. One of the most important discoveries for decentralized organization mechanism for large-scale WSN is the small-world topology. Popular network models can be classified as relational and spatial networks. By analogy with the small-world phenomenon in social networks, Watts and Strogatz [5] have shown that many real relational networks posses small-world characteristics, that is, small typical separation between two vertices (measured by characteristic path length) and high clustering (measured by clustering coefficient). But wireless networks are spatial graphs that tend to be much more clustered than random networks and have much higher path length characteristics. As stated in [6], Ahmed had established a relationship between small world graphs and wireless networks. Their findings indicate that by adding a few short cuts, with only a small fraction (25%-4%) of the network diameter, the degrees of separation may be reduced drastically. Another related work is [7], where the authors identify three common types of hardware heterogeneity: computational heterogeneity-some nodes having more computational power than the others, link heterogeneity-some nodes having a direct and highly reliable connection to the sink node, and energy heterogeneity-some nodes having unlimited energy supplies. G Sharma [8] had investigated the use of limited infrastructure, in the form of wires, for improving the energy efficiency of a WSN. Cavalcanti et al. [9] have applied the small world concept to ad hoc networks by adding a fraction of special nodes equipped with two radios, a short-range radio and a long-range one, operating in different frequency. Guidoni et al. [] have studied theoretical models (TRAM and TDASM) in which the shortcuts are added and also presented their distributed on-line versions (ORAM and ODASM) to build a heterogeneous sensor network with small world features Advances in information Sciences and Service Sciences(AISS) Volume3, Number. December 2 doi :.456/AISS.vol3.issue.

2 during its start-up time. In their proposed model, the added shortcuts reduce the latency and increase the network resilience. The MDS-MAP [] localization scheme, based on the classical metric multidimensional scaling (MDS) localization algorithm, can locate the range-based and range-free. The algorithm does not require anchor nodes to obtain high positioning accuracy characteristics. Although classical MDS localization method is preeminent and attractive work, it is not satisfied and cannot well suitable for sensor networks in adverse circumstances. The rest of this work is organized as follows. Section 2 presents some localization problems in traditional WSN with small-world characteristics. Section 3 presents our experiments and results about small-world characteristics of the SWLS scheme. Section 4 provides localization results for the SWLS method. Section 5 presents our conclusions. 2. Localization problem of small-world in traditional WSN In WSN, location information plays significantly role in the monitoring activities. Equally, localization is a crucial part for a well-constructed WSN with small-world characteristics. Recently numerous localization algorithms for WSN have been proposed. These localization algorithms can be divided into range-based and range-free [2] methods. The range-based method determines the distance between two different sensor nodes based on a variety of information, such as point-to-point distance and angle information. These methods often can achieve to the relatively high positioning accuracy, but this makes sensor node cost increased and consumes limited battery resources yet. In ranged-free methods, the sensor nodes without location information (called normal nodes) gather location information from nodes with known locations (called anchors) and estimate their own locations according to the location information of the anchors. It has more advantages in cost and power consumption compared with rang-based method. In the trilateration of wireless sensor networks, to overcome the affection of localization error caused by the selection of beacon nodes, a selective strategy of beacon nodes based on the angle information is proposed [3]. Dai et al. [4] have developed a new localization algorithm based on a set of uncorrelated discriminant vectors (SUV). Comparing to the centralized multidimensional localization algorithm MDS-MAP that has been widely used in wireless sensor networks, SUV can improve the localization accuracy and reduce the computing complexity. 2.. MDS-MAP scheme MDS-MAP is consisted of the following three steps: Firstly, compute shortest paths between all pairs of nodes in the region of consideration. The shortest path distances are used to construct the distance matrix for MDS. Secondly, apply classical MDS to the distance matrix, retaining the first 2 largest eigenvalues and eigenvectors to construct a 2- dimensional relative map. At last, given sufficient anchor nodes (3 or more for 2-D networks), the coordinates of the anchors in the relative map are mapped to their absolute coordinates through a linear transformation. The best linear transformation between the absolute positions of the anchors and their positions in the relative map is computed MDS method MDS algorithm consists of the following three steps: 2 (a) Simplification of squared distance matrix D Assuming that D 2 ( X ) represent European squared distance. In 2-dimensional space squared distance matrix constituted by the three nodes is expressed as: 2 2 D( X) c T c T 2 xx T c T c T 2XX T a a a

3 Where xa( xa [ x a x2a x3a]) is column vector of matrix X, is the N-dimensional vector whose elements are all, T is transposed vector of. C is a vector constituted by k a x 2 ia elements T (i.e., the diagonal matrix XX diagonal elements) (b) Double-centralization operation 2 ( ) 2 PD X P. Where matrix P I J ( J n n n (all elements of the matrix is )), this matrix in n the mathematical statistics called centered matrix. (c) Singular value decomposition T T Singular value decomposition for XX, we can get B VAV, then, relative coordinates are /2 changed into X VA. In the calculation process, there may be negative values or in eigenvalues of the B, then select first r largest eigenvalues and corresponding eigenvectors to calculate the relative /2 coordinates in B, X r QA r r,when the distance matrix D without or very small error, X r basically reflects the nodes relative position in the network SWLS algorithm MDS-MAP often outperforms another method when nodes are positioned relatively uniformly in space, especially when the number of anchors is low. However, MDS-MAP has inherent shortage on large-scale WSN and is therefore of limited utility in many applications. Such as,figure. is the neighbor relationship graph of all nodes in WSN. Black solid circle are called unknown node. Red * nodes represents anchor node. nodes are placed randomly in the regular m square area. There are 45 anchor nodes and communication radius is 58m, which leads to an average connectivity of.3. In other words, this graph is a large-scale network topology with sparse distance matrix. It is often can encounter for Group A phenomenon in large-scale network topological structure. In large sparse networks, there is a phenomenon that a node group only depends on a fraction of nodes that located in one direction to keep communication with whole network. We put this phenomenon called Group A. Figure. The Group A phenomenon in large-scale WSN topological structure Like many existing methods, MDS-MAP does not work well on large sparse networks, where the Group A phenomenon seriously deteriorates localization results. The primary cause of unfavorable factors is the third step of MDS algorithm (Singular value decomposition). When select first r largest eigenvalues and corresponding eigenvectors to calculate the relative coordinates in B, eigenvalues associated with nodes of Group A will be neglected and ignored due to corresponding eigenvalues are very little. Combine with Figure. and MDS algorithm, an improved algorithm is presented.

4 The algorithm consists of the following two steps: firstly, we select one or more nodes as the initial node. Secondly, we make these elected node communication with others nodes of the range a-b-c-d-ef-a (except for Group A) randomly. It is a significant effect when these elected node can communication with others nodes of the range c-d-e-f-c (except for Group A). There are many methods of detecting edge node can easily help us to find the topology of Group A in distribution graph of large-scale WSN. Such as, based on the local voronoi polygons, Zhang use the - hop neighbor nodes to test node in marginal location [5]. Wang use node connectivity information to find the edge node through the establishment of the shortest path tree [6], and so on. 3. Small world simulation and analysis Wireless sensor networks are spatial graphs that tend to be much more clustered than random networks and have much higher path length characteristics. The random rewiring technique has two main drawbacks. Firstly, form the practical point of view, it is not easy to remove a link in WSN. Secondly, the average distance between pairs of vertices on the graph is poorly defined. In the random addition model (RAM [7] ), we start again with a regular lattice, but now instead of rewiring each shortcut with probability p, we add shortcuts between pairs of vertices chosen uniformly at random but we do not remove any shortcuts from the regular lattice. This model builds small world networks that preserve the high cluster coefficient, as in a regular graph, and the characteristics of a short path length, as in a random graph. 3.. Small world model simulation If the deployment of nodes in the monitoring area is done using a uniform distribution, we can consider that the connectivity graph of the network is similar to the regular graph. Therefore, it is possible to decrease of nodes by adding some shortcuts, i.e., introducing a set of powerful communication sensors. To introduce the small world property to a WSN, we use unicast links to create the shortcuts. The endpoint nodes of these shortcuts should operate in two distinct frequencies, one for the communication among with powerful communication sensors and another one for the communication with the no powerful communication sensors. In this way, long distance transmissions will not interfere in the communication of these nodes. We start our experiments by investigating the following layouts of wireless sensor networks. Without loss of generality, we choose a setting of 2 nodes over a m square area. The communication range is 58m. The communication range of powerful communication sensors is 5m, i.e., an order of magnitude higher than the other sensors. The green line segment represent addition lines that help us to improve the localization of Group A. Topology of WSN is the relationship graph of every node pairs and illustrates the shortcuts created in a WSN using the random addition model. The shortcut generation is done by adding unicast links with a probability p. Red line segment represent shortcut in the graph. When p=. in Figure.2, the network is similar to a regular graph. As we increase the value of the probability p, the original network starts showing the small world characteristics (Figure.3 and Figure.4), and later, random graph characteristics (Figure.5). Topology of WSN,p=. Topology of WSN,p= Figure 2. When p=., the network is similar to a regular graph Figure 3. When p=., network starts showing small world characteristics

5 Topology of WSN,p=. Topology of WSN,p= Figure 4. When p=., the original network shows the best obvious small world characteristics Figure 5. When p=., the network starts showing the random graph characteristics 2 nodes,46 anchors,radio Range:58m C(p)/C() L(p)/L() Figure 6. Reduction of path length and clustering versus probability of link addition 3.2. Small world model analysis For every probability of link addition p, the average path length L, and the clustering coefficient C are measured. For the original case, where p= (without link addition), these values are denoted as L(), and C(), respectively. For other values of p we get L(p), and C(p), respectively. In all simulation results, the ratio L(p)/L() and C(p)/C() is calculated. These ratios represent reduction in length or clustering with increased by adding a fraction of shortcuts in the original regular graph. Results are shown in Figure.6. We note several observations on this result. First, values for clustering and path length of the original graphs (p=) are quite high as compared to those of random graphs. Second, we observe a very consistent trend among all the experiments and across all topologies. There is a clear distinction between the reaction of the path length and clustering to link addition. The path length reduction occurs quite drastically for.2% to 2% of link addition. Further link addition does not contribute much to reducing the path length. For example, addition of.2% of the link results in 25% reduction in L. For p<.8, the average minimum path length is reduced.2 times and the clustering coefficient is the same as the regular graph. When p=., the average minimum path length decreases about 2 times and the clustering coefficient only.2 times. Again the network exhibits small world characteristics. When the value of the probability is., the average minimum path length is reduced about 4 times and the clustering coefficient only.5 times, and the network still keeps its small world characteristics. This suggests that by addition a very small number of random links the path length is drastically reduced without affecting the structure of the network. These results are consistent with the small world graph phenomenon.

6 4. Localization scheme for the WSN with small-world models One of the most significant evaluation factors in the localization technology is localization accuracy, which refers to the precision degree of the calculated information of unknown node obtained by localization algorithm or system. In WSN, localization error is generally used as a quantitative description of localization accuracy. Localization error for WSN can be categorized as either absolute error or relative error. The absolute error refers to difference value between the calculated location of unknown node obtained by localization algorithm or system and actual location. We suppose that d i represent difference value between calculated location and actual location of the node i in the 2-dimensional networks, then, N d denotes the mean localization error of network with N i i N unknown nodes. 4.. SWLS localization error simulation Figure.7 shows the real localization error map of the original distribution. 2 nodes are placed randomly in center m square area. There are 46 anchor nodes among them and communication radius is 58m, which leads to average connectivity of.57 and average neighbor anchor nodes number of network:.45. The circles represent the true locations of the nodes, and the solid lines represent the errors of the estimated position from the true position. The longer the line, the larger the error. The overall localization error is.39. Figure.8 shows localization error map of Fig.3 (p=.). The overall localization error is.263. The example demonstrates that MDS-MAP performs very badly on the original random distribution topologies, but SWLS works well on small world model topologies when addition a very small number of random links the path length is drastically reduced without affecting the structure of the network Average localization error analysis In these experiments, we assess the average-case performance of localization methods. For each of several different types of network, the algorithms are run on many randomly generated examples. Figure.9 shows the average performance of SWLS using proximity information as a function of link addition probability p and localization error. Among them, 2 nodes randomly uniformly distribute in the m square area. There are 46 anchor nodes among them, communication radius: 58m. When p<., the localization error are all more than 3%. In other words, it reaches over 3% and make algorithm disable. When p>. SWLS algorithm s maximum error is less 3%, in line with localization accuracy of the standard algorithm. 2 localization error 2 localization error Figure 7. Localization error map of the original distribution (p=) Figure 8. Localization error map of the small world model (p=.)

7 .9 2 nodes, 46 anchors, Radio Range:58m Localization Error 3%.9 2 nodes, p=.,radio Range:58m regular network small world model Localization Error,% Localization Error,% the value of the probability p Figure 9. The average performance of SWLS (using proximity information as a function of link addition probability p and localization error) the number of anchor node Figure. We vary the anchor ratio to see its impact on the mean error In Figure., we vary the anchor ratio to see its impact on the mean error. The area size of the WSN is m. The total number of sensor nodes is 2. We vary the number of anchors from 5 to 275. As the number of anchors increases, the mean error decreases. For n<5 (n represent the number of anchor node), the both average localization error are reached over 3% and make algorithm disable. But localization errors of regular graph are all more than 5%. In other words, in this case algorithm is completely ineffective. The decreasing curve tends to become smooth when the number of total anchors is over 5. When the ratio of the anchors goes over a certain degree, the size of the estimative region cannot be greatly reduced, and thus, the impact becomes smaller. The SWLS method is more stable compared to regular networks because its mean error range is much smaller than regular network. 5. Conclusions To reduce the energy consumption and communication cost and improve the accuracy of the estimated location, an evolving localization method (SWLS) has been proposed based on small world model, which is one of the most important model for complex network theory and has been wisely used in WSN. In the proposed scheme, we have applied the small world concept to WSN by adding a few shortcuts. Simulations results have shown that SWLS can reduce the average path length, thus reducing the average energy expenditure. Furthermore, we have proposed a MDS-based scheme to correct the localization problem of the large WSN, thus improving the accuracy of the estimated location. Analysis and simulation have shown that the proposed scheme can achieve better accuracy than other environments with reasonable communication expenditure. 6. Acknowledgment This work is supported by National Natural Science Foundation of China under Grant No , and and Key Projects in the Science & Technology Pillar Program of Jiangxi Province of China under Grant No. 2BBG References [] F. Akyildiz, W. Su, Y. Sankarasubramaniam, and E. Cayici, Wireless Sensor Networks: a survey, Computer Networks Journal, Vol. 38, No. 4, pp , 22. [2] D. Estrin, D. Culler, K. Pister, and G. Sukhatme, Connecting the Physical World with Pervasive Networks, IEEE Pervasive Computing, Vol., No., pp , 22. [3] G. J. Pottie and W. J. Kaiser, Wireless Integrated Network Sensors, Communications of the ACM, Vol. 43, No. 5, pp. 5-58, 2.

8 [4] LIU Mei, HUANG Dao-ping, XU Xiao-ling, Node Task Allocation based on PSO in WSN Multitarget Tracking, AISS: Advances in Information Sciences and Service Sciences, Vol. 2, No. 2, pp. 3-8, 2. [5] D. J. Watts and S. H. Strogatz, Collective dynamics of small-world networks, Nature, Vol. 393, pp , 998. [6] Ahmed Helmy, Small worlds in wireless networks, IEEE Communications Letters, Vol. 6, No., pp , 23. [7] M. Yarvis, N. Kushalnagar, H. Singh, A. Rangarajan, Y. Liu, and S. Singh, Exploiting heterogeneity in sensor networks, IEEE INFOCOM, March, pp , 25. [8] G. Sharma and R. Mazumdar, A case for hybrid sensor networks, Proc. of ACM International Symposium on Mobile Ad Hoc Networking and Computing (MobiHoc 6), pp , 26. [9] D. Cavalcanti, D. Agrawal, J. Kelner, D.Sadok, Exploiting the small world effect to increase connectivity in wireless ad hoc networks, Proc. of the th International Conference on Telecommunications(ICT 4), Lecture Notes in Computer Science, Vol. 324, pp , 24. [] D.L. Guidoni, R.A. Mini, A.A.Loureiro, On the design of resilient heterogeneous wireless sensor networks based on small world concepts Computer Networks, Computer Networks, Vol. 54, No. 8, pp , 2. [] Y. Shang, W. Ruml, and Y. Zhang, Localization from Mere Connectivity, MobiHoc'3, Annapolis, Maryland, USA, June, pp.-3, 23. [2] T. He, C. Huang, B.M. Blum, J.A. stankovic, and T. Abdelzaher, Range-Free Localization Schemes for Large Scale Sensor Networks, MobiCom'3, San Diego, CA, USA, September, pp.4-9, 23. [3] Wen-yuan Liu, En-shuang Wang, Zi-jun Chen, Lin Wang, An Improved DV-Hop Localization Algorithm based on The Selection of Beacon Nodes, JCIT: Journal of Convergence Information Technology, Vol. 5, No. 9, pp , 2. [4] Huan Dai, Zhaomin Zhu, Xiaofeng Gu, Distributed Localization Algorithm Based on Statistical Uncorrelated Vectors, AISS: Advances in Information Sciences and Service Sciences, Vol. 3, No. 8, pp , 2. [5] Zhang Chi, Zhang Yanchao, Fang Yuguang, Detecting Coverage Boundary Nodes in Wireless Sensor Networks, Proc. of IEEE International Conference on Networking, Sensing and Control, FL, USA, pp , 26. [6] Wang Yue, Gao Jie, Mitchell Joseph SB, Boundary Recognition in Sensor Networks by Topological Methods, Proc. of International Conference on Mobile Computing and Networking, Los Angeles, USA, pp.22-33, 26. [7] M.E.J. Newman, D.J. Watts, Scaling and percolation in the small world network model, Physical Review E. Vol.6, No. 6, pp , 999.