## 4 Optimized Hidden Node Detection Paradigm
### Hidden Node Detection
In this case, there is a possibility that two nodes can be active at same time and initiate the neighbor node discovery process. Therefore, we use a scheduling method to control the wake up process of two nodes at the same time. During the scheduling, the nodes are required to be synchronized with each other and report to the coordination node. During the scheduling, each receiving node chooses time slots and obtains the data during those time slots. The time slot process is performed without contradicting the schedule of the other node. This is the reason that the neighbor nodes are subdivided into different subdivisions, where each node chooses its slot assigned to that subdivision. Each sensor node decides randomly when to initiate the transmission of a HELLO message. If its message does not strike with another HELLO message, the node is referred to as a discovered node. We can also determine residual energy and the load of each node after the node discovery process occurs. Let us assume that each sensor node communicates at the distance of the single-hop node to detect the hidden nodes. Each sensor node sends the HELLO message 'Hm' at the distance 'd' within the subdivision 'Sd' and is located at the N \(\times\) N area of WMSN. The residual energy of the two types of multimedia sensor nodes, the coordinator node 'C' and the non-coordinator node 'Cn', can be determined as follows. The coordinator node performs four types of jobs that include the synchronization with newly joined nodes, broadcasting the information of newly joined nodes inside the subdivision, scheduling the transmission of subdivision, and data collection from non-coordinator nodes of the subdivision. The synchronization process between the newly joined node and the coordinator is explained in Algorithm 1. ```
1. Initialization: (\(C_{n1}\): coordinator node-1; \(C_{n2}\): coordinator node-2; \(N_{j}\): newly joined-node; \(B_{m}\): beacon message for joining the subdivision; \(S_{n}\): node synchronization process; \(N_{sdl}\): subdivision of the network; \(\ell\): listening)
2. Input: (\(B_{m}\))
3. Output: (\(S_{n}\))
4. Set \(N_{j}\) attempts for \(N_{sd}\) // New node intends to join the subdivision of the network
5. \(N_{j}\perp B_{m}\) // New node sends beacon message for joining the network
6. \(B_{m}\)\(\ell\)\(C_{n1}\) &&\(C_{n2}\) // Beacon message sent by new node, but it is heard/listened by two coordinator nodes when two subdivisions are overlapped. 7. _If \(C_{n1}\)\(\ell\)\(B_{m}\)\(\in\)\(N_{j}\)_ then // If coordinator node-1 gets beacon message from new node for joining the subdivision. Figure 2: Coordination node synchronization process. Here, we determine the energy consumed for four types of jobs. Thus, the residual energy of 'C' and 'Cn' can be calculated as follows:

\[C_{es}=\left[d^{2}\left\{\left(M_{s}\times\left(E_{r}\right)\right)+\left(M_{s} \times\left(E_{a}\right)\right)\right\}\times S_{n}\right] \tag{3}\]

Equation (3) shows the consumed energy by coordinator node for synchronization:

\[E_{b}=E_{r}+E_{a} \tag{4}\]

Equation (4) shows the consumed energy for broadcasting the message (disclosing the information of newly joined nodes to the subdivision nodes):

\[E_{s}=\sum_{S_{n}=1}^{k}\left(E_{r}+E_{a}\right)\times d^{2} \tag{5}\]

Equation (5) shows the consumed energy by coordinator node for scheduling with subdivision nodes:

\[E_{dc}=\left[d^{2}\left\{\left(M_{s}\times\left(E_{r}\right)\right)+\left(M_{s }\times\left(E_{a}\right)\right)\right\}\times S_{n}\right]^{2} \tag{6}\]

Equation (6) shows the consumed energy by coordinator node for collecting and forwarding the data. We can determine the residual energy of the coordinator node and non-coordinator nodes based on the energy consumption for four tasks given by Equations (7) and (8), respectively:

\[C_{re}=C_{ie}-\left(C_{es}+E_{b}+E_{s}+E_{dc}\right) \tag{7}\]

\[NC_{re}=C_{ie}-\left(C_{es}+E_{b}+E_{dc}\right) \tag{8}\]

Determining the node's load is significant for hidden node discovery.