# Energy-Efficient Hybrid Routing Protocol for IoT Communication Systems in 5G and Beyond
## 4 Proposed Methodology
### Hybrid Cluster Construction Phase  
Central station position impacts the cluster chain formation or structure of the network topology. Moreover, it affects the overall energy consumption of nodes. This will affect the quality and efficiency of the network. To alleviate the aforementioned problems, a procedure of chain construction (see Figure 3 for details) is proposed. This procedure allows the created chain topology to adapt to the diverse positions of the central station. In MIMO-HC a projection method is used to create the chain to avoid abnormal cluster chain topology.  
Each node projects its displacement vector in every cluster and all nodes in each cluster are ordered by the principal value of the vector. The principal vector is defined as (4).  
Figure 2: Selection of Cluster Head.  
\[\vec{v}=\begin{cases}(x_{M},0)&\quad\text{if }x_{a}=0\\ (0,y_{M})&\quad\text{if }y_{a}=0\\ (-1,\frac{x_{M}}{y_{M}})&\quad\text{otherwise}\end{cases} \tag{4}\]  
where:  
* (\(x_{M}\), \(y_{M}\)) refers to the position of midpoint (M) of network region.
* \(x_{a}\) and \(y_{a}\) are the x and y symbol for else vector known as \(\vec{a}\) defined in (5), used to link the central station with the network midpoint (M), where (\(x_{B}\), \(y_{B}\)) denotes the location of central station. \[\vec{a}=(x_{B}-x_{M},y_{B}-y_{M})\] (5)  
Figure 3 demonstrates flow chart of the proposed cluster chain formation and the steps are summarized below.  
1. All the report messages from the sensors distributed across a network are gathered by the central station.
2. The central station estimates the position of these distributed nodes according to the obtained signal strength.
3. Based on received Cluster Head Competition Radius value \(R_{c}\), central station decides type of communication topology within certain cluster by identified threshold value _Th._
4. if the Cluster Head competition diameter \(R_{c}>Th\), nodes within cluster wait for random time if no matrix received from the central station, nodes communicate their data directly to their respective Cluster Head.
5. if the Cluster Head competition diameter \(R_{c}\leq Th\), central station computes the chain construction as described in Section 4.2.
6. The central station computes \(\vec{a}\) and \(\vec{v}\bot\vec{a}\).
7. For each node in the cluster, central station computes the vector \(\vec{s_{j}}\), which connects the sensor node \(s_{j}\) with the midpoint of the network area.
8. The projection of \(\vec{s_{j}}\) onto \(\vec{v}\) is computed by the central station using the following Equation (6) \[P_{j}(s_{j})=\frac{\vec{v}.\vec{s_{j}}}{|\vec{v}|}.\] (6)  
The central station constructs a matrix and transmits it to every sensor node when the node projection calculation concludes. The matrix includes ordered sensor nodes on every cluster according to the increasing value of the projection range. The obtained ordered projection value allows nodes on every cluster to build a chain schema. Figure 2 demonstrates the selection process of Cluster Head and is explained as follows Figure 4 is an illustration of the projection approach. Here, the vector for the sensor node \(\vec{s_{4}}\) at the third cluster is calculated by central station. Moreover, it computes \(P_{j}(s_{j})\), which indicates the value of projection (marked by the red line color) of sensor node \(\vec{s_{4}}\) onto \(\vec{v}\) using (6). The same method applies to the other cluster nodes. Next, nodes in the cluster 3 are ordered according to the increasing value of the projection range and followed by construction of the chain topology.