# A Novel Bitrate Adaptation Method for Heterogeneous Wireless Body Area Networks
## 4 Heterogeneous WBAN Simulator
### The Results of Measurements Used in the Simulator
#### 4.2.6 Noise Characteristics of the Radio Interfaces  
Simulations of the WBANs or WSNs requires the determination of the signal power level, which implies the boundary correct reception of the packets [21; 22]. The issue of adaptive allocation of the data streams by means of a dynamic change of transmission rate requires estimating the noise characteristics of the NB and UWB interfaces as a function of the bitrate. It was decided that these noise characteristics should be measured, without considering the values given by manufacturers [26; 27; 43]. This allowed a better representation of the real PER in the analyzed WBAN. The measurements of both RIs were carried out in an indoor environment, obtaining about 50,000 values for the selected transmission rates, i.e.,  
* 50 kbps, 100 kbps, and 200 kbps for the NB interface;
* 850 kbps and 6800 kbps for the UWB interface. The measured data set allowed the noise characteristics of both RIs for PER at \(10^{-3}\), \(10^{-2}\), and \(10^{-1}\) levels at selected transmission bitrates to be determined. Figure 4: The exponential regression function fitted to the empirical measurement data. The NB interface is characterized by the possibility of a smooth change of bitrate in the range of 10 kbps-200 kbps. Therefore, the measured noise characteristic is represented by a liner function, which is determined using a linear regression, minimizing the SEE between the maximal points of normal distributions fitted to the empirical data obtained for selected bitrates. In Figure 5, the method for determining the noise characteristics of the NB interface from empirical measurements for an exemplary PER = \(10^{-3}\) is presented. However, the value of the slope of the determined linear function is \(a~{}=~{}0.125\), and the intercept term is dependent on the PER, i.e., \(b~{}=~{}-76.6\) for PER = \(10^{-3}\), \(b~{}=~{}-78.9\) for PER = \(10^{-2}\), and \(b~{}=~{}-80.0\) for PER = \(10^{-1}\). A similar method was used for the UWB interface--the only difference is that it takes only discrete values for two rates, in accordance with the capabilities of the DWM1000 module [27; 28]. The average value, \(\mu\), of the fitted normal distribution to the empirical data was assumed as a threshold value for PER. This method, for an exemplary PER = \(10^{-3}\), is graphically presented in Figure 6.  
Figure 5: The method for determining the noise characteristics of the NB interface from the data of empirical measurements for an exemplary PER = \(10^{-3}\). Figure 6: The method for determining the noise characteristics of the UWB interface from the data of empirical measurements for an exemplary packet error rate (PER) = \(10^{-3}\). The obtained discrete noise characteristic values of the UWB interface are \(b_{850}~{}=~{}-3.9\) and \(b_{6800}~{}=~{}-89.7\) for PER = \(10^{-3}\), \(b_{850}~{}=~{}-94.4\) and \(b_{6800}~{}=~{}-90.2\) for PER = \(10^{-2}\), and \(b_{850}~{}=~{}-94.9\) and \(b_{6800}~{}=~{}-90.6\) for PER = \(10^{-1}\). Descriptions of research works and simulations of WBANs and WSNs found in the literature often assume that the decision of the lost packet is based on a single threshold value of the interfaces' noise characteristics. Thus, the probability of receiving the packet, \(P_{REC}(P_{0})\), can be determined by:  
\[P_{REC}(P_{0})=\left\{ \begin{array}{ll}1,&P_{0}~{}\geq~{}P_{TH}~{},\\ 0,&P_{0}<\!P_{TH}~{},\end{array} \right. \tag{15}\]  
where \(P_{0}\) is the received signal strength, and the threshold value, \(P_{TH}\), should be chosen from the set of determined noise characteristic values for the selected bitrate. This is because, in real conditions, the receipt of a packet with a certain power level is a random event, which is confirmed by different thresholds for different fixed PER levels. The differentiation in the packet received probability as a function of several power thresholds was proposed as follows:  
\[P_{REC}(P_{0})=