# Clustering-Based Channel Allocation Method for Mitigating Inter-WBAN Interference
## 5 Performance Evaluation  
In this section, we evaluate the proposed method through extensive simulation studies. We randomly deploy a set of WBANs in a 10 m \(\times\) 10 m area \(\mathcal{S}\). Specifically, we select both the x-coordinate and the y-coordinate of each WBAN from [0,10 m] according to the uniform distribution. By considering the width of a human body [29], we make the distance between any two WBANs be larger than 0.5 m. We set the number of channels available for WBANs to 13. We also set \(\delta_{m}=0.3\) and \(\delta_{d}=3\) m. The transmission power of sensor nodes in each WBAN is set to \(p_{i}=p=1\) mW. The length of a time slot is set to 10 s.  
We evaluate the performance of the proposed method in terms of the data rate per Hertz (i.e., \(\gamma_{i}\)) by quantitatively comparing it with those obtained by two alternatives. The first alternative is proposed in [26] where a graph is partitioned into a set of clusters by the KNN method, and a channel is allocated to each cluster by the graph coloring method. Once a channel is assigned to a cluster, the WBANs belonging to the same cluster share the same channel in an FDMA manner. Hereafter, we will call the first alternative KNN. In the second alternative, each WBAN randomly selects a channel from \([1,|K|]\) regardless of the other WBANs. Henceforth, we will call the second alternative RAND. In Figure 1, we show how each method allocates a channel to a WBAN when \(|N|=100\). Each dot represents a location of a WBAN. Except Figure 1c, each color of a dot in Figure 1 represents the channel allocated to a WBAN. The color of a dot in Figure 1c represents the cluster that a WBAN belongs to. In other words, if two WBANs are painted with the same color, they belong to the same cluster. When RAND is used, WBANs randomly select a channel to use independently of the other WBANs. Thus, RAND distributes the channels uniformly over \(\mathcal{S}\). KNN allocates a channel not to a WBAN but to a cluster formed by the K-nearest neighbor method. Thus, the WBANs belonging to the same cluster share the same channel in an FDMA manner. In contrast, our method allocates different channels to the WBANs in the same cluster to reduce the interference among the WBANs using the same channel. The differences in the way of allocating channels result in the differences in the total interference and the total data rates. In Figure 2, we show how the average SIR experienced by the WBANs in \(\mathcal{S}\) varies according to the number of WBANs in the area. The number of available channels is limited. Therefore, SIR decreases as the number of WBANs increases. KNN avoids the inter-cluster interference by allocating different channels to different clusters. Therefore, a WBAN achieves the largest SIR when KNN is used. However, the data rate obtained by a WBAN is influenced not only by the SIR but also by the amount of bandwidth used by the WBAN. To inspect the effect of the channel sharing, we compare the data rate obtained by a WBAN in Figure 3. The number of WBANs in a cluster increases with the number of coexisting WBANs \(|N|\). Correspondingly, in the case of KNN, the amount of a channel bandwidth that a WBAN in a cluster can use decreases as \(|N|\) increases. Therefore, we can observe in Figure 3 that the data rates achieved by KNN are the smallest for all \(|N|\). This is attributed to the fact that as the number of WBANs increases, the gain obtained by increasing the SIR is outweighed by the loss caused by sharing a channel in an FDMA manner. When RAND is used, each WBAN chooses a channel randomly irrespective of the other WBANs. Therefore, among the WBANs in \(N_{i}\), the number of WBANs that select the same channel as the one chosen by a WBAN \(i\) increases with \(|N_{i}|\). Since \(|N_{i}|\) also increases with \(|N|\), the data rates achieved by RAND decrease with \(|N|\). In contrast, our method groups the WBANs that will interfere with each other when they use the same channel.