# Characterization of the Body-to-Body Propagation Channel for Subjects during Sports Activities
## 5 Performance Analysis
### Outage Probability  
The outage probability \(p_{out}\) is defined as the probability that a receiver will not be able to decode the transmitted information correctly. This happens when the received signal has a \(SNR\) below a threshold value \(SNR_{0}\), required for correct decoding, and can be expressed as [23]  
\[p_{out}=\Pr(SNR\leq SNR_{0}). \tag{6}\]  
The threshold value \(SNR_{0}\), depends on the sensitivity of the receiver \(S_{r}\), and can be expressed as  
\[SNR_{0}=\frac{S_{r}}{kTBN_{f}}. \tag{7}\]  
Figure 12: CDFs of channel capacity \(C\) for different average received power \(\overline{P}_{r}\). (a) running; (b) cycling.  
Figure 13: CDFs of channel capacity \(C\) for all scenarios during running and cycling activities with average received power \(\overline{P}_{r}=16\) pW.  
As in channel capacity, the \(SNR\) in (6) varies with the received signal power \(P_{r}\), making the outage probability \(p_{out}\), a random variable. Again, we use the CDFs obtained in Section 4 from the simulation model as well as the measured results, and values in Table 4 to simulate and analyze the outage probability, relative to the receiver sensitivity \(S_{r}\).  
Figure 14 shows outage probabilities for different average received powers (\(\overline{P}_{r}\)) in relation to the receiver sensitivity. Considering the running activity in Figure 13(a), we can observe the same trend as in instantaneous channel capacity with Scenario 1 (subject behind the other) having lower outage probability than Scenario 2 (subject beside the other), with the same average received power and receiver sensitivity. This is the same for the cycling activity in which Scenario 1 (subject behind the other) has the lowest outage probability under the same conditions, Figure 13(b). As with channel capacity, the effect of the stability of the arms on the performance of the channels is seen in Figure 15, where the outage probabilities of the two activities are plotted together. Cycling shows lower outage probabilities for all scenarios under the same receiver sensitivity.  
these kinds of activities, were considered. Due to the on-off nature of the channels in hand, a TSSMM approach was used to develop a simulation model that was validated using the measured data in terms of first and second order statistics, showing good agreement.  
The CDFs obtained from the simulation model, as well as the measured results, were then used to conduct performance analysis of the channels in terms of channel capacity and outage probability. Cycling activities showed better performance than running activities for having higher channel capacity and lower outage probability regardless of the speed of cycling being significantly higher. This is mainly because, during cycling, the arms where the transceivers were attached are more stable. The positive effect of the stability of the arms was also seen in LCR in which cycling showed a smaller fading variation compared to running.  
In general, these kinds of measurement campaigns and the analysis performed in this study are important in characterizing the transmission channel in hand. They give an aspect to the engineers on the challenges involved in communicating through such channels, and assist in deciding the appropriate solution. Furthermore, the performance analysis completed gives insight, which is important for system design.  
This work was supported by the Norwegian University of Science and Technology.  
[PERSON], [PERSON], and [PERSON] conceived and designed the measurement campaign; [PERSON] made the measurement device, conducted the measurement campaign, analyzed the data, and wrote the manuscript. [PERSON] and [PERSON] supported and supervised the research as well as proofread the manuscript.  
The authors declare no conflict of interest.