1396 IEEE COMMUNICATIONS LETTERS, VOL. 16, NO. 9, SEPTEMBER 2012 Distance Based Thresholds for Cluster Head Selection in Wireless Sensor Networks Sang H. Kang, Senior Member, IEEE, and Thinh Nguyen, Member, IEEE Abstract—Central to the cluster-based routing protocols is the cluster head (CH) selection procedure that allows even distribution of energy consumption among the sensors, and therefore prolonging the lifespan of a sensor network. We propose a distributed CH selection algorithm that takes into account the distances from sensors to a base station that optimally balances the energy consumption among the sensors. NS-2 simulations show that our proposed scheme outperforms existing algorithms in terms of the average node lifespan and the time to first node death. Index Terms—Wireless sensor network, cluster, energy con- sumption, distance to base station. I. I NTRODUCTION W IRELESS Sensor Networks (WSN) are often char- acterized by unattended self-organization of non- rechargeable nodes. To prolong the network lifespan of WSNs, cluster-based routing protocols are often used to obtain load balance and to reduce communication volume in a distributed manner. Low Energy Adaptive Clustering Hierarchy (LEACH) [1] is one of the most promising cluster-based routing proto- cols. LEACH divides the network into several clusters of nodes. Through a cluster head (CH) selection procedure, each node in the network has an equal chance of becoming a CH overall. Each CH gathers and processes data from its members, then forwards the aggregate data to the base station (BS). In this way, LEACH attempts to balance the energy consumption among all the nodes. However, if the BS is far away from the sensor field, the energy expense for the CH to send data to the BS increases according to the 4-th power of its distance to the BS [1]. As such, even though all the nodes have an equal chance of becoming a CH, the ones far away from the BS will run out of energy before the closer ones. Therefore, in order to further balance the energy consumption, the probability of a node becoming a CH should be computed based on its distance to the BS. Recently, several distance-based CH selection algorithms have been proposed. In [2], a CH election algorithm is proposed using the minimum and maximum of the distance Manuscript received March 2, 2012. The associate editor coordinating the review of this letter and approving it for publication was I.-R. Chen. S. H. Kang was supported by the Basic Science Program through the National Research Foundation of Korea funded by the Ministry of Education, Science and Technology (No. 2011-0026363). T. Nguyen was supported by NSF (0834775) and NSF-CAREER (845476). S. H. Kang is with the Department of Electrical and Computer Engineering, University of Seoul, Seoul, Korea (e-mail: shkang@uos.ac.kr). T. Nguyen is with the School of Electrical Engineering and Com- puter Science, Oregon State University, Corvallis, Oregon, USA (e-mail: thinhq@eecs.oregonstate.edu). Digital Object Identifier 10.1109/LCOMM.2012.073112.120450 to the BS. In [3], the authors investigate inner-CH multi- hop routing using Dijkstra’s algorithm. In [4], the relative distance to the BS is considered with a weighting factor. In [5], far zone heads are adopted for multi-hop routing; but the interference between the cluster and its far zone needs to be addressed. Note that all the aforementioned approaches are heuristic based on the intuition that the far away nodes should communicate relatively less than the closer ones. Rather than using a heuristic approach, we propose a dis- tributed LEACH-based CH selection algorithm in which nodes are self-selected to become CHs with different probabilities based on their distances to the BS, in such a way that the energy consumption among the nodes are balanced. This is in contrast with the original LEACH protocol where all the nodes are self-selected to become CHs with a constant pre- designed probability, and thus is suboptimal. Next, we briefly describe the LEACH protocol. II. THE LEACH ROUTING PROTOCOL Assume there are N sensor nodes deployed randomly in a square of M × M [m 2 ]. All nodes start with an equal amount of energy. Each node is assumed to perform power control depending on the distance between the transmitter and receiver. LEACH adopts the following energy model: A node transmitting an l-bit message over a distance d [m] will dissipate an energy amount E T (l, d) E T (l, d)=  l(E e + ǫ f d 2 ), if d<δ l(E e + ǫ m d 4 ), if d ≥ δ, (1) where E e [J/bit] represents the energy being dissipated to operate the circuitry per bit, ǫ f [J/bit/m 2 ] and ǫ m [J/bit/m 4 ] denote the factors in Friss’ free space model and the typical multi-path model, respectively, and δ =  ǫ f /ǫ m . The energy dissipation for receiving an l-bit message is determined by E R (l)= lE e . (2) When a node listens to the medium for t [sec], it’s energy consumption is modeled as tE L , where energy dissipation per unit time, E L [Joules/sec], is assumed to be constant for the sake of simplicity. In LEACH, time is divided into rounds, r =0, 1, 2, ··· . The number of CHs in each round is a random variable with expectation k, which is a pre-calculated value as a system parameter. Let p = k/N be the desired percentage of CHs (0 ≤ p ≤ 1). Let us use [·] to denote rounding off throughout this letter. LEACH groups [1/p] successive rounds together to form a group of rounds (GOR). Let G(r) be the set of nodes that have not been CHs within the GOR including the current 1089-7798/12$31.00 c  2012 IEEE