# An Eccentricity Based Data Routing Protocol with Uniform Node Distribution in 3D WSN
## 1 Introduction  
Emerging in technology and sensor devices, the WSN range of usage in applications has been increasing globally such examples as Internet of Things (IoT) [1]. WSN consists of low-powered sensor nodes with sensing, computation and wireless communication capabilities. The constraints of sensor nodes pose a number of conceptual and optimization problems in different applications [2]. Numerous data routing and power management protocols have been proposed, where energy consumption is a vital issue. Most of the researches on WSNs are still based on two-dimensional (2D) planes [3; 4] while sensor node deployment in the real world may require 3D plane network structures. Such examples are ocean column monitoring [5], water quality monitoring [6], weather forecasting [7], climate monitoring [8] and so on, where the sensor nodes are required to be placed at different depths of the ocean and at different levels in the atmosphere, thus creating 3D WSNs. From these aspects, 3D WSN can be implemented in various potential applications in different environments. Primarily, minimizing the number of deployed nodes to achieve full-coverage and connectivity is important, because senor node deployment in 3D space is comparatively expensive. In this regard, several literatures have been studied addressing the optimization problem [9; 10]. The major constraints of sensor nodes are the limited power and limited transmission range that require an energy-efficient routing strategy for a faraway BS or Sink. To resolve this issue, several datarouting protocols have been proposed. Routing protocols based on clustering potentially are the most effective to reduce energy consumption of nodes [11] and have been widely accepted. The key strategy of this approach implies data gathering at a cluster head (CH) node from cluster members (CMs) and a hierarchical data forwarding towards the sink using single-hop or multi-hop depending on the network circumstances. Although this approach is delay tolerant, it is effective to apply a time division multiple access (TDMA) schedule to assign the time slots for the constituted nodes to communicate with each other and that can avoid the collisions of channels and interferences in the network. In addition, it guarantees reliable data communication with less packet loss, unlike other routing policies. However, the performance of a clustering-based routing protocol in terms of network lifetime may vary upon the deployed nodes in different dimensions (such as in 2D or in 3D network fields). Besides, node distribution strategy (e.g., random and uniform/nonuniform or deterministic) depending on the applications is one of the key factors affecting the network lifetime. The random and nonuniform node distribution poses a network to form unequal size clusters in distributed clustering networks. Therefore, the energy consumption of nodes in different clusters is imbalanced and results in a shorter steady state and network lifetime. In this paper, we propose the eccentricity based data routing (EDR) protocol [12] with uniform node distribution in a 3D WSN where the nodes are deployed in such a way that the prior divided 3D subspaces of the network contain equal numbers of member nodes. An eccentricity region based routing centroid (RC) node election in each individual subspace is applied that not only minimizes the intra-subspace communication costs but also balances the energy consumption of nodes. To minimize the cost of RC nodes election, a quasi-static period based RC nodes election is combined with periodic election. RC node during its quasi-static period continues as the RC that is defined by a threshold energy level. This policy continues until a certain period of time depending on the local circumstance of a subspace. It reduces the broadcasting of control messages which are economically viable considering the energy consumption of nodes.