A Minimum-energy Path-preserving Topology Control Algorithm for Wireless Sensor Networks

International Journal of Automation and Computing 6(3), August 2009, 295-300 DOI: 10.1007/s11633-009-0295-0 A Minimum-energy Path-preserving Topology Control Algorithm for Wireless Sensor Networks Jin-Zhao Lin 1, 2, Xian Zhou 3 Yun Li 1 1 Research Center for Wireless Sensor Networks, Chongqing University of Posts and Telecommunications, Chongqing 400065, PRC 2 Institute of Communication and TT & C, Chongqing University, Chongqing 400044, PRC 3 Key Laboratory of Optical Communication and Lightwave Technologies, Ministry of Education, Beijing University of Posts and Telecommunications, Beijing 100876, PRC Abstract: The topology control strategies of wireless sensor networks are very important for reducing the energy consumption of sensor nodes and prolonging the life-span of networks. In this paper, we put forward a minimum-energy path-preserving topology control (MPTC) algorithm based on a concept of none k-redundant edges. MPTC not only resolves the problem of excessive energy consumption because of the unclosed region in small minimum-energy communication network (SMECN), but also preserves at least one minimum-energy path between every pair of nodes in a wireless sensor network. We also propose an energy-efficient reconfiguration protocol that maintains the minimum-energy path property in the case where the network topology changes dynamically. Finally, we demonstrate the performance improvements of our algorithm through simulation. Keywords: Wireless sensor networks, topology control, power-efficient, minimum energy property, k-redundant edges. 1 Introduction A wireless sensor network is composed of a great deal of low-cost sensor nodes in the monitored area, where communication between two nodes may go through multiple consecutive wireless links. It has wide civil and military applications. Because the power of sensor nodes is limited, network protocols that minimize energy consumption is a major goal in the design of wireless sensor networks. By virtue of topology control, power-efficient algorithms for maintaining network connectivity and optimizing performance metrics such as network life and throughput can be designed [1 5] Li et al. [1] considered a cone-based topologycontrol algorithm, where a node u tries to find the minimum transmission power P u,a to ensure that there are some nodes that u can reach with power P u,a in every cone of degree α around u. Yin et al. [2] proposed a two-level topology control strategy that integrates active subnetwork [3] and short hops [4] methods to achieve further energy saving. Busse et al. [5] described a new topology and energy control algorithm (TECA) that uses a very simple clustering approach and connects these clusters in a very energy-efficient way. Li and Halpem [6] proposed an effective topology control algorithm, called small minimum-energy communication network (SMECN). But SMECN has a flaw around the unclosed region which could result in excessive energy consumption. We put forward a new topology control algorithm, minimum-energy path-preserving topology control (MPTC), which not only resolves the problem but also ensures that the network has a minimum-energy path prop- Manuscript received Nobember 10, 2008; revised February 4, 2009 This work was supported by by National Natural Science Foundation of China (No. 60702055), Program for New Century Excellent Talents in University (NCET-07-0914), the Science and Technology Research Project of Chongqing Municipal Education Commission of China (KJ070521). *Corresponding author. E-mail address: linjz@cqupt.edu.cn erty. The rest of the paper is organized as follows. Section 2 gives the network model. Section 3 simply introduces and analyzes the SMECN algorithm, and then discusses the problems of this algorithm. Section 4 puts forward a new algorithm, MPTC. Section 5 shows how to use MPTC to deal with topology changes using only local message exchanges. Section 6 gives the results of simulations, showing that using the network constructed by MPTC, energy can be saved. Section 7 concludes our paper. Notations. F (u, p): A region around u which can be reached with power p. Loc(v): Physical location of node v. N F (u,p) : A set of nodes in F (u, p) and N F (u,p) = {v V : Loc(v) F (u, p)}. A: A set of all the nodes that u has found so far. M: New nodes found by u in the current iteration. R u v: Relay region {(x, y) : C(u, v, (x, y)) C(u, (x, y))}. η: The direct-transmission region of node u induced by the currently known nodes. R F (u) : The final direct-transmission region of u induced by all nodes. N(u): A set of the final neighbors of node u. P (u): The final transmitted power of node u computed by MPTC. 2 Model We assume that all nodes in a wireless sensor network are deployed in a two-dimensional area, where no two nodes are in the same physical location. Each node knows its own location, and has a unique identification code. A transmission between nodes u and v takes power p(u, v) = α d(u, v) n for some appropriate constant α, where n 2 is the path-loss exponent of outdoor radio propaga-

296 International Journal of Automation and Computing 6(3), August 2009 tion models [7], and d(u, v) is the distance between u and v. Due to the very short transmission distance of the nodes in the wireless sensor network, we set n at 4. When each node of the wireless sensor network uses its biggest power in working, this topology is called the biggest power topology, expressed as a graph G max = (V max, E max) in which V max is the nodes congregation of the network and E max = {(u, v), α d(u, v) 2 p max}. In a graph G max = (V max, E max), if there is a path P AT H(u, v) = (u = u 0, u 1,, u n 1, u n = v), with length P AT H(u, v) = n, the consumed energy, when messages are delivered through this path, is n 1 C(P AT H(u, v)) = nc + p(u i, u i+1) (1) where c is the consumed energy when a node receives messages, usually smaller than the transmission power of the sensor node. Transmitting at the maximum power requires a great deal of energy. To reduce energy consumption, we invoke a subgraph G of G max such that [6] 1) G consists of all the nodes in G max but has less edges; 2) if u and v are connected in G max, they are still connected in G; and 3) a node u can transmit to all its neighbors in G using less power than is required to transmit to all its neighbors in G max. Indeed, what we need is a subnetwork G of G max with these properties where the power for a node to transmit to its neighbors in G max (possibly over several hops) is minimal. A subnetwork G is said to have the minimum-energy property [6] if the following holds: for every pair (u, v) of nodes that are connected in G max, the subgraph G has only a path between u and v, which is the minimum-energy path among all the paths between u and v in G max. i=0 3 Key definitions and the shortcoming of SMECN 3.1 Some key definitions Definition 1. There exist an edge (u, w) E max and a path P AT H(u, w) in G max, P AT H(u, w) = k, k > 1. If C(P AT H(u, w)) < C(u, w), then the edge (u, w) is a k- redundant edge. Fig. 1 gives an example of a two-redundant edge. Fig. 1 Two-redundant edge (u, w) Definition 2. Given a node v, the relay region of the transmit-relay node pair (u, v) is the physical region R u v such that relaying from v to any point in R u v takes less power than direct transmission [6]. R u v = {γ : C(u, v, γ) C(u, γ)}. Definition 3. Let F = F (u, p) be a region where the node u can reach and cover with transmission power p and let N F be a set of nodes located in F, i.e., N F = {v V : Loc(v) F }. Define R F (u) as the direct-transmission region of node u [6] R F (u) = (F (u, p) R u v). (2) v N F According to Definition 2, R F (u) denotes a region in which transmitting directly to any point consumes less power than relaying through any node in F. Fig. 2 shows R F (u) of node u for a given N F = {u, v, m, t}. Fig. 2 R F (u) for a circular region F (u, p) 3.2 The shortcoming of SMECN Based on the above definitions, Li and Halpem [6] proposed an effective topology control algorithm, called a small minimum-energy communication network (SMECN). For the details of SMECN, please refer to [6]. Here, we analyze the shortcomings of SMECN. The purpose of the SMECN is to find the minimal transmission power p of a random node u, which ensures that the region F (u, p) encloses the final direct-transmission region R F (u). The SMECN makes transmission power of the node u increase gradually until F (u, p) η or p increases to the maximal power of u. The final transmitted power of u is set at min{p : F (u, p) η}. After all of the nodes in the wireless sensor network compute their transmission power in this way, the wireless networks are thought to contain their subnetworks that do not include two-redundant edges and have minimum-energy property [6]. The careful implementations of the SMECN is shown in Algorithm 1. According to the SMECN, the direct-transmission regions R F (u) can be divided into two different types, closed region (see Fig. 3 (a)) and unclosed region (see Fig. 3 (b)). If direct-transmission region R F (u) of the node u is a closed region, then SMECN can find a transmitted power p (0 < p < p max) of u that satisfies F (u, p) R F (u). However, if R F (u) is an unclosed region, then SMECN cannot find a transmitted power p (0 < p < p max) of u that satisfies F (u, p) R F (u) unless it has increased to the maximal transmitted power p max of u and then SMECN will use p max as the transmitted power of u. Therefore, the existence of the unclosed region must result in bigger transmitted power set by SMECN. As a result, the nodes will consume more energy. When a network exits from the situation of the nodes locations maldistribution, the disadvantage of SMECN is especially obvious. Herein, after we give a new topology control algorithm MPTC to avoid the excessive consumption of energy.

J. Z. Lin et al. / A Minimum-energy Path-preserving Topology Control Algorithm for Wireless Sensor Networks 297 Algorithm 1. SMECN running at node u. 1. p = p 0; 2. A = ; 3. NonNbrs = ; 4. η = F (u, p max); 5. while F (u, p) η do { 6. p=increase(p); 7. Broadcast Hello message with power p 8. and gather ACK; 9. M = {v Loc(v) F (u, p), v / A, v u }; 10. A = A M; 11. for each v M do 12. for each w A do 13. if Loc(v) R u w then 14. NonNbrs = NonNbrs {v}; 15. else if Loc(w) R u v then 16. NonNbrs = NonNbrs {w}; 17. η = η v M (F (u, p max) R u v); } 18. R F (u) = η; 19. N(u) = A NonNbrs; 20. p(u) = min{p : F (u, p) η}. Fig. 3 (a) Closed region (b) Unclosed region Closed region and unclosed region 4 The MPTC algorithm Different from SMECN, MPTC sets the transmitted power of nodes without judging whether the nodes transmission region covers its direct transmission region. The detailed MPTC algorithm is shown in Algorithm 2, which proceeds in the following main steps. Step 1. For a given node u, u starts the process by broadcasting a Hello message at maximum power p max, stating its own position. If the other nodes receive this message, the responding u with the ACK message states their location. Let NBR(u) be the set of nodes that respond to u. Step 2. Node u broadcasts a Hello message from an initial power p = p 0, gets ACK from all nodes in F (u, p), and establishes a set M that registers all nodes in F (u, p). Step 3. Let NBR(u) = NBR(u) M. For every node w NBR(u) and v N, MPTC checks whether edge (u, w) is a two-redundant edge or not, which means that MPTC checks whether C(u, v, w) < C(u, w). If the edge (u, w) is a two-redundant edge, then NBR(u) = NBR(u) {w}. Step 4. MPTC checks whether the set NBR(u) =. If not, node u will transmit with more power p and turn to step Step 2 until NBR(u) =. After NBR(u) =, MPTC sets its final transmitted power as transmitted power of u. Algorithm 2. MPTC running at node u. 1 p = p 0; 2 M = ; N = ; 3 Broadcast Hello message with power P max 4 and gather ACK; 5 NBR(u) = {v p(u, v) P max}; 6 while NBR(u) do 7 p = Increase (p); 8 Broadcast Hello message with power p 9 and gather ACK; 10 N = {v Loc(v) F (u, p), v / M, v u}; 11 M = M N; 12 NBR(u) = NBR(u) M; 13 for each w NBR(u) do 14 for each v N do 15 if C(u, w) > C(u, v, w) then 16 NBR(u) = NBR(u) {w}; 17 NBR = {v Loc(v) F (u, p), v u}; 18 P (u) = p. When all nodes in a wireless sensor network run the MPTC algorithm to determine their transmission power, we can obtain a subgraph G = (V, E) of G max, in which V denotes a set of all nodes in the network, E denotes a set of edges satisfying E E max. The subgraph G of G max constructed by MPTC has the following feature. Theorem 1. If the G max can ensure the connectivity of the wireless sensor network, then the subgraph G = (V, E) can also ensure the connectivity of the network and has the minimum-energy property. Proof. 1) Connectivity We assume that there is a P AT H(u, v) = (u = u 0, u 1,, u n 1, u n = v) in G max. We firstly prove that nodes u i and u i+1 (i = (0,, n 1)) are connected in graph G. According to the MPTC algorithm shown in Algorithm 2 if edge(u i, u i+1) is not a two-redundant edge, we reserve the this edge in graph G. Otherwise, if the edge(u i, u i+1) is a two-redundant edge, there are paths P AT H (u i, u i+1) = (u i, wi 1, wi 2,, wi m, u i+1) in G, and C(P AT H (u i, u i+1)) < C(edge(u i, u i+1)). (3) So, if u i and u i+1 are connected in G max, they are also

298 International Journal of Automation and Computing 6(3), August 2009 connected in G. We can find a path between u and v in G like P AT H (u, v)=(u = u 0, w0, 1 w0, 2, w m 0 0, u 1, w1, 1 w1, 2, w m 1 1,, u n 1, wn 1, 1 wn 1, 2, w m n 1 n 1,un = v). (4) The above process proves that for a given pair of nodes u and v, if there is a path between them in G max, there is also a path between u and v in subgraph G. Therefore, if G max is connected, then so is G. 2) minimum-energy property We assume that there is a minimum-energy path between u and v in G max, P AT H(u, v) = (u = u 0, u 1,, u n 1, u n = v), which is not in G. There is at least an edge(u i, u i+1) (i = (0, 1,, n 1)) in P AT H(u, v) which is not included in G. Due to the connectivity of G, there is another path P AT H (u i, u i+1)=(u i, wi 1, wi 2,, wi m, u i+1) in G to connect node u i and node u i+1. According to MPTC algorithm, it is not hard to show C(P AT H (u i, u i+1)) < C(edge(u i, u i+1)), so there is another path between u and v in G max, P AT H (u, v)=(u = u 0, u 1,, u i, wi 1, wi 2,, wi m, u i+1,, u n 1, u n = v), and C(P AT H (u, v)) < C(P AT H(u, v)), which means that P AT H(u, v) = (u = u 0, u 1,, u n 1, u n = v) is not a minimum-energy path between u and v in G max. It is contrary to the foregoing assumption. Hence we can conclude that G has the minimum-energy path property. 5 Reconfiguration of the minimumenergy subgraph In a multihop wireless sensor network, the topology is dynamic because nodes are mobile, i.e., some nodes will die and new nodes will join in the network. In this section, we propose a reconfiguration process of a minimum-energy subgraph when the network topology is changed. We assume that each node uses a neighbor discovery protocol (NDP) [6], a periodic message that provides all its neighbors with its current position in order to detect changes in the topology of the wireless sensor network. A node u sends out the message with P max to reach all the nodes, and collects all the location-information of its neighbors. Once a node detects a change, it may need to update its set of neighbors by a reconfiguration protocol of minimum-energy subgraph. There are three types of events triggering the reconfiguration protocol: 1) A dead event D u(v): The node v, a neighbor of node u, cannot be detected by node u. 2) A joining event J u(v): Node u detects a new neighbor v. 3) A moving event M u(v): Node u detects its neighbor v moving to a new location. When the node detects these three types of events, it runs the process of the reconfiguration protocol of MPTC as follows. If a single dead event D u(v) or joining event J u(v) is detected, let NBR(u) = NBR(u) {v} or NBR(u) = NBR(u) + {v} where NBR(u) is a set of neighbors searched by u lastly. Then, they both run the MPTC algorithm from the 4th line to the 18th line in Algorithm 2. If a moving event M u(v) is detected, the protocol updates the information of the location of node v firstly, and then let NBR(u) = NBR(u). Similarly, run the MPTC algorithm from the 4th line to the 18th line in Algorithm 2. The reconfiguration protocol of the minimum-energy subgraph avoids the excessive energy-consumption that results from a whole network rerunning MPTC when it detects only a small portion of the nodes changes. 6 Evaluations In this section, we evaluate the performance of MPTC through simulation. 6.1 Simulation environment The simulation is conducted on simulator NS-2 [8]. We suppose that there are 30 100 nodes placed uniformly at random in a rectangular region of 1000 m 1000 m. Each node has an omni-directional antenna with 0 gain, 1.5 m above the node. According to the needs of simulation, we set ten levels between the minimum transmitted power ( 34.75 dbw) and the maximum transmitted power ( 14.75 dbw), corresponding to the transmission radii of nodes from 25 m to 250 m. The detailed simulation parameters are listed in Table 1, in which AODV denotes Ad hoc on-demand distance vector routing. Table 1 Simulation parameters Parameters Description Value prop Radio-propagation model TwoRayGround CPThresh Capture threshold 10 db CSThresh The carrier sense threshold 108 dbw RXThresh Receive threshold 94 dbw freq Carrier frequency 914 MHz Rb Transmission raw bandwidth 2 MHz Rp Wireless routing AODV [9] ifqlen Max packet in interface queue 50 6.2 Simulation results Let us see the topology structure of the network. Fig. 4 depicts a network s topology structure with 100 nodes controlled by MaxPower (every node transmits messages using its maximum power), SMECN, and MPTC. We can see from Fig. 4 that the topology structure constructed by MPTC is sparser, which helps to reduce potential collisions and increases the power effectiveness of nodes. (a) MaxPower

J. Z. Lin et al. / A Minimum-energy Path-preserving Topology Control Algorithm for Wireless Sensor Networks 299 (b) SMECN packets. We have used the following application scenario. The application traffic is assumed to have constant bit rate (CBR), and the application packets are all 512 bytes. The packet sending interval decreases from 100 ms to 9 ms; that is, packet arrival rate increases from 40.96 kb/s to 455.11 kb/s. The change of average end-to-end delay of packets based on different traffic loads is shown in Fig. 6. At the beginning, the packet arrival rate is relatively low and the traffic load of the network is at the low level. Because the MaxPower lets every node transmit messages using its maximum power, which makes the retransmission times of a packet less than MPTC and SMECN from the source node to the destination node, the delay time of MaxPower is shorter than SMECN and MPTC. However, along with the increase of the network s traffic load, the delay time of MPTC becomes gradually shorter than the other two algorithms. Because the increasing traffic load will intensify the competition for channels between different packets, MPTC can effectively control the number of each node s neighbors, thus decreasing the mutual interference between nodes and the probability of packet collisions. (c) MPTC Fig. 4 The topology structure of network controlled by Max- Power, MPTC, and SMECN The node degree is an important factor for the performance of a network. Low node degree is favorable for improving the network capability and reducing the probability of packet collision. Fig. 5 presents the average number of neighbors of a network that consumes receiver power c with 0 or 2 mw in the above different algorithms. It can be seen that the node degree rapidly increases with increasing network density in MaxPower. However, the average number of neighbors controlled by MPTC almost remains stable and smeller than those formed by MaxPower and SMECN in all cases. Fig. 6 Average end to end delay Fig. 5 Average degree of nodes Then, we would like to see how the different traffic loads in the network affect the average end-to-end delay of Reducing power consumption and prolonging the network lifetime are two very important targets of wireless sensor networks. Therefore, we consider the change in network lifetime (the time from beginning of simulation to death of the node). The application scenario is as follows. We assume that each node in our simulation has an initial energy of 1 J. The packet sending interval is decreasing from 1 s to 0.1 s, that is to say, packet arrival rate is increasing from 4.096 kb/s to 40.96 kb/s. The effect of a network s lifetime on the different network s traffic load is shown in Fig. 7. We can see the all network lifetimes obtained using the above three algorithms are reducing with the traffic load added. However, MPTC s outperforms MaxPower and SMECN in the aspects of prolonged network lifetime. The above simulation results show that MPTC significantly outperforms SMECN. Moreover, in [6], SMECN has been proven to have better performance than MECN and cone-based distributed topology-control with optimization (OPT-CBTC) in such aspects as network lifetime, and average number of neighbors. So MPTC also outperforms MECN and OPT-CBTC.

300 International Journal of Automation and Computing 6(3), August 2009 Fig. 7 7 Conclusions The lifetime of network The most important purpose in the design of wireless sensor networks is to save the energy of the nodes. Topology control can reduce the consumption of sensor nodes, optimize the performance of networks and prolong the life span of the networks through adjusting the transmission power of sensor nodes. This paper puts forward a new topology control algorithm MPTC of wireless sensor networks, based on the concept of k-redundant edge. It not only avoids excess energy consumption resulting from the unclosed region in SMECN, but also ensures the connectivity of the network with the minimum-energy path property. In addition, we have proposed an energy-efficient reconfiguration protocol that maintains the above minimum-energy path property even if the network topology changes dynamically. Finally, we have shown the performance improvements of MPTC over SMECN and MaxPower through simulation. References [1] L. Li, J. Y. Halpern, P. Bahl, Y. M. Wang, R. Wattenhofer. A Cone-based Distributed Topology-control Algorithm for Wireless Multi-hop Networks. IEEE/ACM Transactions on Networking, vol. 13, no. 1, pp. 147 159, 2005. [2] B. Yin, H. Shi, Y. Shang. A Two-level Strategy for Topology Control in Wireless Sensor Networks. In Proceedings of the 11th International Conference on Parallel and Distributed Systems, IEEE Press, vol. 2, pp. 358 362, 2005. [3] B. Chen, K. Jamieson, H. Balakrishnan, R. Morris. Span: An Energy-efficient Coordination Algorithm for Topology Maintenance in Ad Hoc Wireless Networks. Mobile Computing and Networking, vol. 8, no. 5, pp. 481 494, 2002. [4] J. Liu, B. Li. Distributed Topology Control in Wireless Sensor Networks with Asymmetric Links. In Proceedings of IEEE (GLOBECOM) Global Telecommunications Conference, vol. 3, pp. 1257 1262, 2003. [5] M. Busse, T. Haenselmann, W. Effelsberg. TECA: A Topology and Energy Control Algorithm for Wireless Sensor Networks. In Proceedings of the 9th ACM International Symposium on Modeling Analysis and Simulation of Wireless and Mobile Systems, Terromolinos, Spain, pp. 317 321, 2006. [6] L. Li, J. Y. Halpern. A Minimum-energy Preserving Topology-control Algorithm. IEEE Transactions on Wireless Communications, vol. 3, no. 3, pp. 910 921, 2004. [7] T. S. Rappaport. Wireless Communications: Principles and Practice, Englewood Cliffs, Prentice-Hall, NJ, USA, 1996. [8] VINT Project. The Network Simulator ns 2, [Online], Available: http://www.isi.edu/nsnam/ns. [9] C. E. Perkins, E. M. Royer. Ad-hoc On-demand Distance Vector Routing. In Proceedings of the 2nd IEEE Workshop Mobile Computing Systems Application, pp. 90 100, 1999. Jin-Zhao Lin received the B. A. degree in wireless engineering from Xi an Jiaotong University, PRC in 1991, and the M. A. and Ph. D. degrees of circuit and system from Chongqing University, PRC in 1995 and 2001, respectively. He had also a 3 year post-doctor experience in automation science and engineering. He is now a full professor in Chongqing University of Posts and Telecommunications, and a part-time professor in Chongqing University. His research interests include signal processing, wireless communication, and mobile network. networks. Xian Zhou received the M. A. degree in communication and information system from Chongqing University of Posts and Telecommunications, PRC in 2008. She is currently a Ph. D. candidate in Beijing University of Posts and Telecommunications, PRC. Her research interests include sensor networks and fiber communication. Yun Li received the B. A. and M. A. degrees from Southwest University and Chongqing University of Posts and Telecommunications, PRC in 1997 and 2000, respectively, and the Ph. D. degree from University of Electronic Science and Technology, PRC in 2004. He is currently a full professor in Chongqing University of Posts and Telecommunications. His research interests include wireless