# Energy-Efficient Hybrid Routing Protocol for IoT Communication Systems in 5G and Beyond
## 4 Proposed Methodology
### Inter-Cluster Sub-Optimal Multi-Hop Routing  
In this section, the proposed energy-aware, inter-cluster multi-hop routing method is discussed. This proposed method ensures that there are sub-optimal routes among cluster heads and the central station employed every once in a while for a connection.  
Figure 4: The method of projection for chain formation.  
Figure 3: Formation of hybrid cluster.  
Selecting the optimum route among the cluster heads may lead to the consumption of energy levels across the route. This causes a considerable differences in the energy levels between nodes, which eventually induce partitioning of the network. Therefore, we have developed an energy-aware and a probabilistic multi-hop routing protocol to connect the cluster heads. Through the suggested MIMO-HC, we are attempting to detect several paths from the cluster heads to the central station, and the probability of selection is allocated to every route. Using the probability, one of the routes for each interval of data transfer from the Cluster Head to the central station is chosen randomly (\(P_{s_{i}s_{j}}\)), see Equation (10). Figure 5 describes the proposed inter-cluster sub-optimal multi-hop routing.  
A simple energy metric, which was employed in [29], is adopted to meet our target. This metric provides details of the cost of using the cluster heads' route and residual energy across the route (7).  
\[Cost_{ij}=e_{ij}^{c1}E_{residual_{i}}^{c2} \tag{7}\]  
where  
* \(cost_{ij}\) symbolizes the cost metric among the cluster heads \(i\) and the Cluster Head \(j\).
* \(e_{ij}\) is the used energy for transferring and delivering on a route.
* \(E_{residual}\) symbolizes the estimated current remaining energy of a Cluster Head.
* weighted factors represented by two symbols (\(c1\) and \(c2\)).  
Figure 6 is the flow chart for the inter-cluster multi-hop routing topology. Upon identifying the Cluster Head and its belonging member nodes for the current running round, the central station creates a routing table (\(RT\)) and next broadcasts it to the intended Cluster Head. Before transmitting the generated routing table to the network, the central station attaches a set of Cluster Head IDs to the \(RT\) and at the same time determines the cost field in the \(RT\) with value zero (i.e., \(Cost(CS)=0\)).  
Figure 5: Description of inter-cluster sub-optimal multi-hop routing.  
Cluster Head \(s_{j}\) calculates the energy metric for the transmitted \(RT\) by intermediate Cluster Head \(s_{i}\) and adds it to the overall cost of the path (8)  
\[Tcost_{s_{i}s_{j}}=Cost_{s_{i}j}+e_{ij}^{c1}Ec_{residual_{i}}^{2}. \tag{8}\]  
Routes that have a very high cost are discarded and not added to the \(RT\). Only the neighboring cluster heads \(s_{i}\) with routes of low cost are added to the routing table \(RT_{j}\) of Cluster Head \(s_{j}\) as shown in Equation (9)  
\[RT_{j}=i|Tcost_{s_{i}s_{j}}\leq c1.(min_{\textbf{k}}(Tcost_{s_{i}s_{j}}). \tag{9}\]  
A probability is given for every Cluster Head \(s_{i}\) included in the \(RT_{j}\) by the Cluster Head \(s_{j}\), where this likelihood has an inverse relation to the cost.  
\[P_{s_{i}s_{j}}=\frac{\frac{1}{Tcost_{s_{i}s_{j}}}}{\sum\limits_{k\in RT_{j}} \frac{1}{Tcost_{s_{k}s_{j}}}} \tag{10}\]  
Later, the average cost of reaching central station via the adjacent cluster heads included in \(RT\) is computed by Cluster Head \(s_{j}\).  
\[Tcost(s_{j})=\sum\limits_{i\in RT_{j}}Tcost_{s_{i}s_{j}}P_{s_{i}s_{j}} \tag{11}\]  
Eventually, the current Cluster Head average cost is applied to the cost field and foreword it towards the next Cluster Head, this process continues to exist till the last Cluster Head is identified.  
The proposed inter-cluster communication protocol specifies a \(Tx\_Th\) threshold value such that when Cluster Head has a range less than or equivalent to \(Tx\_Th\) to the central station, it conveys its data immediately to the central station.  
Figure 6: Inter-cluster sub-optimal multi-hop routing.