# Energy-Efficient Hybrid Routing Protocol for IoT Communication Systems in 5G and Beyond
## 4 Proposed Methodology
### Cluster Head Selection Phase  
The algorithmic flow chart in Figure 2 demonstrates the selection process of Cluster Head and is explained as follows. With a certain power level, a \"\(HELLO\)\" message is transmitted by the central station to every sensor node positioned in the network area. Received signal strength helps every node to estimate its relative distance to the central station, and therefore, generates a hybrid of clusters of uneven size. Upon receiving such a message, nodes would easily compute their Competition Radius and deliver a report containing estimated current residual energy, altered Competition Radius, and the ID of node to central station. In our proposed MIMO-HC, the candidature to becoming the cluster head is determined only if a node contains higher leftover energy than nodes fall in its radius. To build a hybrid clusters with unequally size, every node should determine its own Competition Radius. In MIMO-HC, nodes that have greater remaining energy will handle additional tasks. Thus, the clusters, which are far from the central station with higher leftover energy, use single-hop topology and have greater number of nodes than those in the proximity which use chain topology. To do this, a sensor node with higher leftover energy needs to augment its own Competition Radius as its range to central station increases. On the one hand, nodes with lower residual energy should have a smaller Competition Radius to prevent their early death. The node Competition Radius is computed through the formula of Rc by (3).  
\[R_{C}=[1-\alpha\frac{(d_{max}-d(s_{i},CS)}{(d_{max}-d_{min})}-\beta(1-\frac{E_ {residual}}{E_{max}})]R_{C}^{0} \tag{3}\]  
where:  
* \(d(s_{i},CS)\) symbolizes the range from sensor node \(s_{i}\) to central station,
* \(\alpha\) and \(\beta\) are the weighted factors, where \(0\leq\alpha\leq 1\) and \(0\leq\beta\leq 1\),
* \(R_{C}^{0}\) symbolizes the maximal value of Competition Radius,
* \(E_{residual}\) symbolizes the estimated current residual energy of node \(s_{i}\).
* \(E_{max}\) symbolizes the primary node energy, usually identical for all nodes.
* \(d_{max}\) and \(d_{min}\) represent the maximal and minimal range among both central station and sensor nodes.  
Figure 1: Overview of the proposed MIMO-HC technique.  
Once the central station obtains the notification messages from the sensors, the ultimate Cluster Head is chosen among the candidate nodes. After that central station generates a matrix and sends it out to all sensors distributed on the network. The matrix  
\[\begin{bmatrix}d_{11}^{h}&...&d_{1n}^{h}\\.&d_{ij}^{h}&\\ d_{n1}^{h}&...&d_{nn}^{h}\end{bmatrix}\]  
involves a list of nodes related to a particular cluster \(h\), and the range among the nodes, and the Cluster Head ID where:  
* \(d_{ij}^{h}\) symbolizes the range among node \(i\) and node \(j\).
* \(h\) symbolizes the Cluster Head ID.  
Obtaining the matrix allows every sensor to know easily and accurately their respective Cluster Head and the range to other sensors; hence, the power of transmission can be changed according to the received distance to minimize the consumption of energy.