## 2 Related Work  
There are two types of sensor deployment schemes: structured and unstructured. The difference between these two schemes is that the sensors of an unstructured WSN are randomly deployed (this is usually used in an unreachable environment) while the positions of the sensors in a structured one are pre-determined. In this paper, we focus on the structured scheme. The structured sensor deployment problem has been extensively studied by many researchers, and pioneers deploy such pre-determined WSN in practice, such as WSNs used to monitor Dolmabahce Palace (Istanbul), Torre Aquila (Italy), a local street (Spain), Bird's Nest (China) and a forested nature reserve (USA), see [PERSON] _et al._[1], [PERSON] _et al._[2], [PERSON] _et al._[3], [PERSON] _et al._[4] and [PERSON] _et al._[5], respectively. [PERSON] _et al._[6] claim that deterministic deployment is appropriate for plain and easily accessible fields such as the embassy/museum garden. For this type of deployment, the number of sensors and the topology of WSN are determined in advance. Thus, the associated energy consumption and lifetime of the WSN can be analyzed and optimized before the deployment. [PERSON] _et al._[7], [PERSON] _et al._[8] and [PERSON] [9] divide the target area into multiple rings and analyze the optimal sensor deployment schemes in different rings. [PERSON] [10], [PERSON] _et al._[11], [PERSON] _et al._[12] and [PERSON] _et al._[13] study the structured deployment methods based on grids, and [PERSON] _et al._[13] deployed a WSN based on grids to monitor Dolmabahce Palace in Istanbul. In [10], the advantages and potential applications of hexagon-based WSN are introduced, and the study shows that WSN can gain benefits from the hexagon-based topology in coverage, energy saving, reliability, routing design, _etc._ The deployment of such hexagon-based topology requires to determine the sensor locations according to the coordinate. For those key WSNs with long lifetime requirement, such as the WSN that may be used in the cabin of the next generation airborne networks (see [PERSON] and [PERSON] [11], [PERSON] _et al._[12] and [PERSON] and [PERSON] [14]), it is worthy to deploy sensors according to the optimal deployment scheme. The WSN topologies can be either heterogeneous or homogeneous. Compared with the heterogeneous WSN, the homogeneous one, in which all sensors are the same in sensing capability, communication capability, power capability, _etc._, is convenient and cheap to deploy. Pioneers propose several sensor deployment schemes for homogeneous WSN. For instance, [PERSON] [14] applies the hexagonal grids to investigate the minimal sensor density. He assumes that the whole target area is a circular plane that can be divided into rings with a centered base station. The relationship between the sensor density and the ring radius is studied. However, the exact positions of these sensors are not given, which leads to a large overlap of coverage or no coverage in some areas. [PERSON] _et al._[10] divide the target area into regular hexagonal grids, in which sensors are deployed in the middle of the grids. They indicate that the deployment can achieve the optimal coverage and, at the same time, satisfy the connectivity constraints, but the energy consumption and the success transmission rate of WSN are not considered. [PERSON] _et al._[13] also study the deployment based on the regular hexagonal grids. They address the advantages of their method in coverage, connectivity, reliability and energy consumption, but, to achieve the optimal lifetime and sensor deployment scheme, the distance between the neighboring sensors and the number of sensors deployed are not optimized. Moreover, retransmission, which is an important way to guarantee the success data transmission rate, is ignored in all of the abovementioned research works. In this paper, retransmission, which has a large effect on the energy consumption but is usually neglected in previous works, is taken into account in our deployment-based lifetime optimization.