## 4 Proposed Scheme
### Cluster-Head Rotation  
In a sensor network composed of various types of sensor devices, even if the initial energy may be uniform, heterogeneity will naturally emerge over time. This is due to the varying energy consumption during sensing operations, which differs among sensor nodes depending on their sensing mechanisms. Consequently, cluster-head rotation methods that consider homogeneous network attributes are not practical. Figure 3 demonstrates the simplified problem of achieving maximum cluster lifetime in a cluster consisting of two nodes with heterogeneous parameters. The examples depicted in Figure 3a,b assume that both nodes possess identical initial energy and data rate levels (energy = 0.1 J and packet size = 4000 bits at time = 0). In Figure 3a, a static cluster-head (CH) assignment is used, with node 1 retaining the CH role throughout. Consequently, node 1 depletes its energy more quickly than node 2, leading to node 1's shutdown after 250 cycles. It is crucial to note that time is measured in cycles, where each cycle representsa sensor's operation, from data collection to transmission to the cluster head. Thus, in this instance, the cluster's lifespan is 250 cycles. In contrast, Figure 3b demonstrates that the cluster's lifespan can be extended by rotating the CH role between the nodes. Node 1 serves as CH from cycles 0 to 164, after which node 2 takes over. Both nodes deplete their energy simultaneously after 328 cycles, thus extending the cluster lifespan to 328 cycles. It is important to highlight that the maximum lifespan occurs when both sensor nodes expire at the same time. Figure 3c presents a scenario in which both sensor nodes have different initial energy levels (node 1: 0.1 J, node 2: 0.06 J) while maintaining the same data rate (4000 bits). However, the time gap between the failure of node 1 and node 2 does not optimise the cluster lifespan. To improve this, Figure 3d shows an applied role rotation similar to Figure 3b but with nodes of heterogeneous energy levels. The results in Figure 3d confirm that uncoordinated rotation still yields suboptimal results, emphasising the importance of coordinated role rotation. Finally, Figure 3e shows the results of coordinated role rotation, designed to maximise cluster lifespan and minimise the time between failures of the first and second nodes. This  
Figure 3: Residual energy of nodes in a WSN with varying scenarios of roles; **(a)** Homogeneous energy nodes have fixed roles; **(b)** Homogeneous energy nodes have rotating roles; **(c)** Heterogeneous energy nodes have fixed roles; **(d)** Heterogeneous energy nodes with uncoordinated role rotation; **(e)** Heterogeneous energy nodes with coordinated role rotation. coordinated rotation extends cluster lifespan from 250 to 262 cycles, and achieves greater stability in the network. Figure 4 illustrates the heightened complexity of achieving minimum energy consumption in intra-cluster communication while maintaining operational stability when nodes possess diverse initial energies and packet sizes (e.g., node 1: 5000 bits, node 2: 3000 bits). As shown in Figure 4c, coordinated role rotation yields favourable results, maximising both network lifespan and stability. However, this challenge becomes more significant in large-scale networks with multi-level and multi-parameter heterogeneity, particularly when nodes are separated by varying distances to the next hop. To address this, a new cluster-head rotation scheme is introduced to minimise intra-cluster energy consumption while maximising stability in heterogeneous sensor networks. Assuming the base station (BS) is aware of each node's location, it first calculates the pairwise distances between every node within a cluster. This information is then used to implement a cluster-head rotation policy that balances energy usage and maximises network lifetime.