# Field-Based Optimal Placement of Antennas for Body-Worn Wireless Sensors
## 1 Introduction  
Technological development, especially in the field of sensor technology, highly integrated electronics and telecommunications, allows for the introduction of new solutions in health monitoring of medical patients as well as monitoring of sportsmen, people working in hazardous environments or exposed to hazards at work, and other safety critical contexts [1]. Early solutions used wired sensors, involving wires and connectors, which adversely affected the user's comfort. A more recent approach is to use body-worn wireless sensor networks, known as Wireless Body Area Networks (WBAN) [2; 3]. Due to the development of the integrated circuit technology it is possible to manufacture ever more complex and yet miniature electronic modules (including sensors), small enough to be integrated into clothing. A good example are Flora sensors made by the company Adafruit [4]. Their diameter is less than 45 mm and the weight is 4.4 g. Such clothing, fitted with miniature sensors, electronic devices and computing power of microcontrollers is known as smart clothing or e-textiles [5]. The functions performed by smart clothing may be diverse, including a mobile, remote measurement of humanphysiological parameters, vital signs monitoring, monitoring of physical activity or automatic detection of risks. A comprehensive introduction to WBAN and relevant design issues are provided in [1]. In this paper we discuss optimization of a WBAN system which uses wireless communication technology to monitor physiological and environmental parameters of firefighters and their exposure to hazardous environmental conditions. The system concept is presented in Figure 1. It consists of a head sensor, an arm sensor, and a chest sensor. The head sensor location is fixed in the helmet because it measures blood oxygen saturation (pulse oximetry) on the earlobe, which is one of typical locations used for this type of sensor [6]. The location of the arm node/sensors (accelerometers and a GPS receiver, temperature and humidity sensors) is fixed and determined by our experiments with a firefighter's comfort for a particular design of protective clothing in mind. The chest node is both an on-body sensor and an off-body node which is communicating with on-body components and with the remote monitoring system. The chest node measures the humidity, temperature, and respiratory activity of firefighters and therefore is located on the chest, in a position ensuring a low value of the path loss to the other two on-body sensors to achieve low required RF transmission power and consequently low power consumption leading to an increased network lifetime or less demanding energy harvesting. The objective of our optimization procedure is to minimize the path loss between the chest sensor and the other two sensors: it is achieved by changing the location of the chest sensor within a predefined region, the boundary of which represents a problem constraint. In that respect our optimization problem is significantly different from those where the number of WBAN nodes (sensors and sinks) is greater and network topology as well as routing optimization should be considered, e.g., [7; 8; 9]. We do not assume any empirical-statistical radio wave propagation model as in [9]. We use more accurate computational electromagnetics methods as explained in Section 2.1. The path loss between the chest node and the other two nodes is defined by \(S_{21}\) and \(S_{31}\) which are parameters of the scattering matrix, widely used in the microwave technology. The parameters are defined as:  
\[ \begin{array}{l}S_{21}\ =\ b_{2}/a_{1}\ \ \text{while}\ \ a_{2}\ =\ 0\ \ \text{and}\ \ a_{3}\ =\ 0\\ S_{31}\ =\ b_{3}/a_{1}\ \ \text{while}\ \ a_{2}\ =\ 0\ \ \text{and}\ \ a_{3}\ =\ 0\end{array}  \tag{1}\]  
where: \(a_{i}\)--input signal on port \(i\) and \(b_{j}\)--output signal on port \(j\), which are explained in Figure 2. We assume that the ports for which the scattering parameters are defined are the feeding points of the antennas.