## 1 Introduction  
A wireless sensor network (WSN) consists of plentiful low-power sensor nodes capable of sensing, processing and communicating. These sensor nodes observe the phenomenon at different points in the field, collaborate with each other and send the measured data to the base station (BS). Therefore, WSNs are extremely important in cyber-physical system (CPS) for observing and cognizing the complicated physical world at low cost [1]. However, sensor networks have limited and non-rechargeable energy resources; energy efficiency is a very important issue in designing the network topology, which affects the lifetime of sensor networks greatly. Thus, how to minimize energy consumption and maximize network lifetime are the central concerns when we design protocols for WSNs. Fortunately, these are the main goals of topology control [2, 3]. Roughly speaking, topology control technology can be classified into two types. One is power control, and the other is hierarchical topology control. For the hierarchical topology control, generally, there exist about four methods, _i.e._, clustering methods (e.g., [4, 5, 6]), connected dominating set methods (e.g., [7, 8, 9, 10, 11]), spanning tree methods (e.g., [12, 13, 14]) and spanner methods (e.g., [15, 16]). By topology control, we usually can obtain a simplified topology of a given WSN while reserving connectivity (e.g., [17, 18]) and coverage (e.g., [19, 20, 21]). Moreover, the diameter of the obtained topology cannot be increased any more (e.g., [22]). As a kind of effective topology control method, clustering has proven to be an important way to decrease the energy consumption and to extend the lifetime of WSNs. In a clustering scheme, sensor nodes are grouped into clusters; in each cluster, one node is selected as the leader, named the cluster head (CH), and the other nodes are called cluster members (CMs). Each CM measures physical parameters related to its environment and then sends them to their CHs. When the data from all CMs is arrived, CHs aggregate the data and send it to the BS. On the one hand, since CHs are responsible for receiving and aggregating the data from their CMs and transmitting the aggregated data to the specified destination, the energy consumption is much higher than that of CMs. Thus, to solve the problem, choosing appropriate cluster heads is the key issue when designing a cluster protocol. On the other hand, if CHs send the aggregated data to the BS directly, long-distance transmission will consume a lot of energy and lead to the premature death of CHs. Thus, designing a suitable inter-cluster multi-hop routing tree to forward data is also an important object of a clustering protocol. In this paper, aiming at some energy heterogeneous WSNs where nodes are deployed uniformly, we propose a novel clustering protocol: LECP-CP (local energy consumption prediction-based clustering protocol), in which a new cluster head election algorithm is designed, which uses the predicted local energy consumption ratio of nodes as the parameter to compete for the role of the CH. Thus, the global energy consumption can be optimized by the optimization of the local energy consumption. To further reduce the energy consumption of CHs, we also propose a new inter-cluster communication routing tree construction algorithm, based on the local energy consumption ratio of nodes, as well. In addition, we provide explicit numerical calculations for the optimal cluster radius to minimize the energy consumption of the entire network, which is proven to be more accurate and realistic by theoretical analysis and simulation experiments. The rest of the paper is organized as follows. Section 2 introduces the related works in this field. Section 3 gives the network model. Section 4 presents the local energy consumption prediction-basedclustering protocol in details. Section 5 describes the derivation process of the local energy consumption ratio of nodes in detail. Section 6 analyzes several properties of our algorithms. Section 7 exhibits and analyzes our simulation results.