## 1 Introduction  
With rapid advancement in electronics industry, small inexpensive battery-powered wireless sensors have already started to make an impact on the communication with the physical world. WSN consists of large number of low cost devices to gather information from the diverse kinds of physical phenomenon. The sensors can monitor various entities such as: temperature, pressure, humidity, salinity, metallic objects, and mobility; this monitoring capability can be effectively used in commercial, military, and environmental applications [1; 2; 3; 4; 5; 6; 7; 8; 9; 10; 11]. For these sensor network applications, most research has discussed problems by the deployment of large number of low-cost homogeneous devices. But in practical applications, in order to meet the demands of various applications for the technologies of sensor networks, increasing attentions have been attracted to the researches on heterogeneous WSNs [12]. Heterogeneous WSN is composed of different types of sensor nodes, which are in a wide range of applications [13; 14]. In fact, the heterogeneity is common in the WSNs [15]. The priority should be given to reduce energy dissipation in network operation, improve network load and stability, and prolong network lifetime. Compressive sensing (CS) [16; 17; 18] is a collection of recently proposed sampling methods in information theory. The combination of CS theory with WSNs holds promising improvements to the lifetime of wireless sensors, whereas it reduces global scale communication cost without introducing intensive computation or complicated transmission control. CS states that sparse signal of information in WSNs can be exactly reconstructed from a small number of random linear measurements of information in WSNs [19]. CS provides a new approach to mathematical complexities especially when sparse information is applied. CS tends to recover data vector \(X\in\mathbb{R}^{N}\) with \(N\) number of information form data vector \(Y\in\mathbb{R}^{M}\) with \(M\) number of information such that \(M\ll N\)[20]. This will result in extending the lifetime of the sensor network. Energy consumption in networks can be effectively reduced by organizing clustering sensor nodes, so many energy-efficient routing protocols are designed on the basis of the clustering structure. Currently, a number of distributed clustering protocols are proposed. In accordance with the networks, homogeneous or heterogeneous, to which the protocols are adaptive, clustering protocols can be categorized into homogeneous clustering protocols which assume that all the sensor nodes are identical and heterogeneous clustering protocols which assume that the sensor nodes have different capabilities. Due to the dynamic and complex nature of energy configuration and network evolution, it is very difficult to design a clustering protocol which can save energy and provide reliable data transmission in heterogeneous networks. To overcome the above problems, we propose a new protocol EDACP-CS for heterogeneous WSNs. EDACP-CS includes two phases: the cluster head arrangement phase and the routing phase. In cluster head arrangement phase, all the sensor nodes organize themselves into clusters with one node elected as a cluster head (CH) according to their weighted election probabilities and their distance to the base station (BS) to determine near nodes and far nodes in order to give more chance to nearest nodes to be CHs by modifying the election probability value for each type of nodes. In the routing phase, after receiving the data from the member nodes, each CH compresses the collected data using CS and transfers it to the BS. Simulation results show that our protocol can aggregate data efficiently and reduce energy consumption greatly, prolonging the stability period and the lifetime of the whole network strongly depend on higher values of extra energy during its heterogeneous settings and different transmission ranges. The remainder of the paper is organized as follows: Section 2 presents the related work of the proposed protocol.