# Clustering-Based Channel Allocation Method for Mitigating Inter-WBAN Interference
## 5 Performance Evaluation
After making a set of clusters, our method allocates different channels to the WBANs in the same cluster to mitigate the total interference. Thus, our method achieves higher data rates than the other methods. For example, compared with KNN, our method increases the average data rate provided to a WBAN by 2.2 times when \(|N|=50\). Our method further increases the average data rate by 5.4 times when \(|N|=200\). When compared with RAND, our method increases the average data rate by 1.2 times for all \(|N|\). Figure 1: Comparison of the channel allocation behavior. Each dot represents a location of a WBAN. Except (**c**), where a color of a dot represents a channel allocated to a WBAN. The color of a dot in (**c**) represents a cluster. Thus, in (**c**), the WBANs having the same color belong to the same cluster. Figure 2: Comparison of the average SIR obtained by each method. When \(|N|=200\), RAND and our method seem to produce similar results. To examine the differences between these methods, we inspect the distribution of the data rate of a WBAN (\(\gamma_{i}\)) when \(|N|=200\), which we show in Figure 4. In this figure, we can observe that the proportion of WBANs whose data rates range from 6 to 12 is 61.5% when RAND is used. When our method is used, the proportion of WBANs whose data rates are within the same range increases to 79.5%. In addition, the variance of the data rate achieved by our method is 5.84 which is smaller than 6.58 obtained by RAND. To scrutinize the influence of the channel allocation method, in Figure 5, we compare our method and RAND in terms of the interference imposed on a WBAN when \(|N|=100\). Specifically, for each WBAN \(i\) in a cluster \(j\), we inspect \(D_{i}(t)=\sum_{k\in\mathbb{C}_{j}(t)\wedge N_{i}(t)}I_{i}(t)-\sum_{k\in C(t)- C_{i}(t)\wedge N_{i}(t)}I_{i}(t)\). The first term \(\sum_{k\in\mathbb{C}_{j}(t)\wedge N_{i}(t)}I_{i}(t)\) represents the interference imposed on a WBAN \(i\) in \(C_{j}\) by the other WBANs in the same cluster, while the second term in \(D_{i}(t)\) is the interference imposed on \(i\) by the WBANs in the other clusters. RAND does not construct a set of clusters. Thus, to compare our method with RAND under the same condition, we use the same set of clusters constructed by our method and apply RAND to each cluster. In Figure 5, we can observe that \(D_{i}(t)\leq 0\) when our method is used,  
Figure 4: Comparison of the distribution of \(\gamma_{i}\) when \(|N|=200\). Figure 3: Comparison of the data rate provided to a WBAN. while RAND \(D_{i}(t)\geq 0\) for all \(i\in N(t)\). It indicates that since inter-WBAN interference is affected by the distance between the WBANs using the same channel, we can alleviate the inter-WBAN interference imposed on a WBAN by allocating different channels to the WBANs in the same cluster after partitioning a graph into a set of clusters so that the modularity of the graph is maximized. In Figure 6, we compare our method and RAND in terms of \(Z_{j}(t)=\frac{1}{|C_{j}(t)|}\sum_{i\in C_{j}(t)}D_{i}(t)\). When RAND is used, the total interference among the WBANs in the same cluster \(C_{j}(t)\) is larger than the total interference imposed on all the WBANs in \(C_{j}(t)\) from the WBANs in \(C(t)-C_{j}(t)\). In contrast, when our method is used, \(Z_{j}(t)<0\) for all the clusters. Thus, our method increases the data rate by reducing the interference among the WBANs in the same cluster. In Figure 7, we depict the distribution of the data rate of a WBAN in each cluster when \(|N|=100\). We observe that in terms of the average data rate in a cluster, the differences among the clusters are marginal. We also observe that our channel allocation method does not penalize clusters in terms of the data rates provided to the WBANs in the clusters. To evaluate the performance of our method in a dynamic environment, we enable each WBAN to move during each time slot. Specifically, a WBAN randomly chooses both a movement direction from \([0,360^{\circ}]\) and a movement speed from \([0,3.6\) km/h] according to the Uniform distribution.