## 5 Results and Discussion  
Table 1 summarizes the parameters used in the simulation. We evaluated the performance by adjusting the number of nodes in the network, number of clusters, and network size in appropriate ranges. We consider a square network area in an indoor environment, place the HAP at the center of the area, and randomly distribute the sensor nodes. Assuming all of the sensor nodes to be homogeneous, their EH efficiencies (\(\zeta\)) are all equal to 0.8 [21]. The ratio of energy used for transmission (\(\eta\)) is set to 0.9 for the sensor nodes and 0.7 for the CH. For ease of exposition, we consider a simple distance-dependent path loss model given by \(h_{i}=Gd_{i}^{-7}\) and \(g_{ij}=Gd_{ij}^{-7}\) assuming the channel fading effect to be averaged out over the frame and all of the channels to be reciprocal [22; 23; 24]. Here, \(d_{i}\) is the distance between the HAP and CH \(i\), \(d_{ij}\) is the distance between nodes \(i\) and \(j\), \(G\) refers to the average power attenuation at a reference distance of 1 m and is set to \(-30\) dB, and \(\gamma\) is the path loss exponent, which is set to 2.5 [46]. Moreover, we set the length of the WET slot (\(T_{e}\)) to 5 s and set the lengths of the SWIPT slot (\(T_{s}\)) and WIT slot (\(T_{d}\)) both equal to 0.1 s, assuming the aggregated sensing data to have the same size as the individual sensing data through proper data fusion [47]. For performance comparison, we consider the following five schemes:  
1. _LEACH_: The CH is chosen randomly based on the stochastic threshold algorithm of the LEACH protocol [41]. The other sensor nodes are connected to the nearest CH and do not use SWIPT. 2. _K-means_: The clusters are created using the K-means clustering algorithm, and the CH is chosen as the node closest to the centroid of each cluster. SWIPT is not used. 3. _Non-SWIPT_: The clusters are created using the K-means clustering algorithm, but the CH is chosen as the node that maximize \(R^{\text{noSwipt}}\) given by Equation (6). This scheme is the baseline for checking only the effect of the WPSN without SWIPT. The performance of this scheme is given by Equations (6) and (15). 4. _ENO with PS_: The proposed clustering and CH selection algorithm is used, and PS-based SWIPT is applied. The performance is given by Equations (12) and (18). 5. _ENO with TS_: This scheme is the same as ENO with PS, except that TS-based SWIPT is applied. Figure 3 presents the clustering results of an example case when 300 sensor nodes are deployed randomly and grouped into five clusters in a square network with a width of 30 m. Note that the LEACH protocol is omitted because the CH is randomly selected and continuously changed in LEACH. The size of each node point represents the amount of energy dissipated in the sensor node. The smaller the dot, the less energy is wasted. The results of the K-means algorithm show that the five clusters are geographically well divided. However, there is dissipated energy in most of the nodes because the K-means algorithm does not use SWIPT. Since the non-SWIPT scheme uses the K-means algorithm for clustering, the cluster set is the same, but the selected CH is different. This behavior occurs because the non-SWIPT scheme considers \(R_{i}\), as shown in Equation (6), and eventually selects the CH that provides a higher rate. In this non-SWIPT case, most of the nodes have the dissipated energy distributions similar to those in the K-means algorithm because SWIPT is not used too. Figure 3c,d show the proposed SWIPT-based ENO schemes. There is no significant difference between the PS and TS methods. It is evident that the clustering results obtained using the proposed schemes are different from those generated using the K-means and non-SWIPT schemes. In addition, there is little energy dissipation at the nodes in the clusters other than Cluster 1 in the lower left corner. This is because each node transfers its remaining energy to the CH through SWIPT and the CH uses it to transmit its data.