# A Lifetime Maximization Relay Selection Scheme in Wireless Body Area Networks
## 1 Introduction  
Wireless Body Area Networks (WBANs) have recently emerged as a subfield development of Wireless Sensor Networks (WSNs) and a promising technology in short-range communication area [1] to provide many important and useful applications in different domains such as vital sign monitoring, interactive gaming, and telemedicine [2; 3; 4]. In general, a WBAN consists of one coordinator and a set of sensor nodes that have to be very simple, tiny and harmless to the human body [5]. These sensor nodes are usually placed in the clothes or on the skin of a person, some even implanted into the body to monitor some certain parameters about human body. At the same time, the coordinator acts as a sink which collects all the information attained by the sensors and communicates it to the user or the remote server for further processing. In order to provide satisfactory services in applications, network lifetime of WBANs ought to be highlighted as a crucial parameter [6; 7]. As we know, sensor nodes deployed in WBANs are minimized in size, which means they are mostly supplied by non-renewable and energy-limited batteries. When one or more devices have to be implanted or worn by a person, enormous stress is caused by the battery replacement/recharging, which, in some cases, may require surgery. Furthermore, each node in WBANs has its unique function that can not be alternatively executed by other nodes. When one sensor runs out of power, WBANs will not perform well or even stop working. As a result, it is a necessity to prolong the lifetime of each sensor node in WBANs to relieve the stress of frequentrecharging/replacement, especially the sensor node that may be exhausted first (The coordinator has sufficient energy compared to sensor nodes). In IEEE 802.15.6 [8], which is specifically designed for WBAN communication, topology is specified commonly as a star topology and can be extended to a two-hop tree topology. This extension indicates that cooperative transmission of a sensor node through a relay is an alternative choice instead of direct one-hop transmission to the coordinator. The authors in [9] have proven that appropriately using cooperative transmission can effectively save energy and prolong the lifetime of sensor nodes that are relatively far away from the coordinator through mathematical analysis and numerical simulation. That is to say, rationally utilizing the combination of direct transmission and cooperative transmission to sensor nodes in WBANs can improve lifetime performance of the whole network. Hence, an appropriate relay selection is of great importance in cooperative transmission strategy to prolong the network lifetime of WBANs. In this paper, a relay selection scheme called the Lifetime Maximization Relay Selection Scheme (short for LMRSS) is proposed to maximize the lifetime of WBANs through formulating and solving an optimization problem where relay selection of each node acts as the optimization variable under the topology constraints specified in the IEEE 802.15.6 standard. The proposed scheme not only regards the transmission depletion condition of each sensor node as relay selection criterion, but also considers the factor of energy difference among sensor nodes according to the fact that sensor nodes deployed on different locations of the human body have different sensing tasks and thus their node sizes and battery capacities may be diverse. Moreover, inferred from the fact that the network can function well only when all the nodes stay alive, in our formulated problem, the aim is to improve the minimum lifetime of sensor nodes within a WBAN, which provides maximum improvement of network lifetime. In more designing detail of our relay selection scheme, we firstly derive that the lifetime of WBANs is a function of relay selection results.