## 5 The Proposed Protocol
### PDFH and SDFH Selection Utilizing the MPA
#### 5.2.3 Optimizing Data Fusion Regrouping (PDFH Reselection) Procedure
Transmission Through Multiple Hops Using an Innovative Relay Data Fusion Cost Function for Improving Routing Technique  
In IoT networks, data fusion is essential for addressing energy consumption challenges, particularly given the energy limitations of SNs. By aggregating and processing raw data locally within the network, data fusion minimizes the amount of data that needs to be transmitted, thereby reducing the energy required for communication, which is directly influenced by packet size and transmission distance. It eliminates redundant data, ensuring that only relevant information is transmitted, and enables localized processing, reducing the reliance on long-distance communication, which consumes exponentially more energy. These efficiencies extend the lifespan of SNs and the network as a whole, making IoT deployments more sustainable and scalable, particularly in energy-sensitive or remote environments where battery replacement is impractical. Data fusion, therefore, plays a critical role in optimizing energy use and enhancing the overall efficiency of IoT systems. In the proposed protocol without routing, PDFHs directly forward the collected data to the sink node after aggregating it from SNs. As a result, PDFHs farther away from the sink node consume more energy and die far sooner than PDFHs closer to the sink. To achieve reliable and effective load balancing and reduce the overhead of communication (i.e., transmission distances), we provide the idea of multi-hop communication to the proposed protocol. It is interesting to note that a DFG-based method is incorporated into an effective multi-hop communication process, in which PDFHs independently gather data from every SN in their DFGs and forward it to the sink node. To effectively send the gathered data to the sink node, PDFHs essentially use intermediary PDFHs as PDFRs, FSDFRs, and SSDFRs. Section 5.5 will go into further information about the function of FSDFRs and SSDFRs. The multi-hop approach employed in the proposed protocol offers reliable, stable, and efficient load balancing by minimizing transmission distances. Taking into account the previous discussion, the proposed protocol has two different types of communication processes: intra-DFG communication and inter-DFG communication. A PDFH and a SDFH are allocated to each DFG when the network is divided into many DFGs for multi-hop inter-DFG communication. PDFH is responsible for managing intra-DFG communication, or communications between DFGMS within that DFG. Part of this PDFH's function is to collect data from DFGMs within its DFG and, based on how far away from the sink node it is, send it there directly if the distance is less than \(d_{o}\), or through an intermediary PDFH (PDFRs and SDFRs) if the distance is greater. In the proposed protocol, the sink node performs the computations required to determine which PDFRs and SDFRs are optimal for each PDFH. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**SN ID** & **Message Arrival Time (ms)** & **Type** & **DFG ID** & **PDFH ID** & **Rank** & **TDMA TS Number** \\ \hline
20 & 10 & “NDFGM” & 6 & 10 & 1 & 1 \\ \hline
16 & 15 & “NDFGM” & 6 & 10 & 2 & 2 \\ \hline
4 & 16 & “NDFGM” & 6 & 10 & 3 & 3 \\ \hline
32 & 20 & “NDFGM” & 6 & 10 & 4 & 4 \\ \hline
10 & 7 & “PDFH” & 6 & 10 & 5 & 5 \\ \hline \hline \end{tabular}
\end{table} 
Table 8: TDMA schedule for intra and inter for DFG 6. This approach significantly enhances inter-DFG communications in scenarios where PDFHs and the sink node are located at significant distances from one another. This reduces energy consumption and increases the network's operational lifetime. Crucially, when selecting a PDFR and a SDFR, the prerequisites that follow must be fulfilled: (1) The Euclidean distance between Candidate PDFR (CPDFR) and PDFH should be as near to \(d_{o}\) as possible in the direction of the sink node (i.e., upstream), provided that it is smaller than \(d_{o}\).